SSAT Middle Level Quiz: Pattern Rules From Sequences

20 questions · exam conditions

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Pattern Rules From SequencesQuestion 1 of 20

Predict the next number: $9, 18, 36, 72, \;?$

144

108

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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Pattern Rules From Sequences

Practice Pattern Rules From Sequences in SSAT Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Pattern Rules From Sequences, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Predict the next number: $9, 18, 36, 72, \;?$

81
90
144 (correct answer)
108

Explanation: This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is multiplied by 2 to produce the next. Choice C is correct because it accurately predicts the next number as 144, showing understanding of geometric progression with a common ratio of 2. Choice A is incorrect because it suggests 81, reflecting a common misconception of switching to a different ratio like 9 times something. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

Question 2

Predict the next number: $64, 32, 16, 8, 4, \;?$

3
2 (correct answer)
1
8

Explanation: This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is divided by 2 to produce the next. Choice B is correct because it accurately predicts the next number as 2, showing understanding of geometric progression with a common ratio of 1/2. Choice A is incorrect because it suggests 3, reflecting a common misconception of switching to arithmetic subtraction. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

Question 3

A sequence follows the pattern: 2, 6, 18, 54, ... Each term after the first is obtained by multiplying the previous term by the same number. What is the next term in the sequence?

108
162 (correct answer)
216
270
324

Explanation: This is a geometric sequence problem, where each term is found by multiplying the previous term by a constant ratio. When you see a sequence with this pattern, your first step is to find the common ratio by dividing any term by the previous term. Let's find the common ratio:

6 ÷ 2 = 3

18 ÷ 6 = 3

, and

54 ÷ 18 = 3

. The common ratio is 3, meaning each term is triple the previous term. To find the next term, multiply 54 by 3:

54 × 3 = 162

. The correct answer is B. Now let's examine why the other choices are incorrect. Choice A (108) represents doubling the previous term instead of tripling it—this would be the pattern if the common ratio were 2, but we established it's 3. Choice C (216) would result from multiplying by 4, suggesting a misidentified common ratio. Choice D (270) would come from multiplying by 5, which is also an incorrect ratio. The key strategy for geometric sequences is always to verify your common ratio using multiple consecutive terms, not just one pair. If you had only checked

6 ÷ 2 = 3

and missed checking the other ratios, you might have been less confident in your answer. Also, double-check your arithmetic—multiplying 54 by 3 carefully ensures you don't fall into a calculation trap. On the SSAT, sequence problems often include distractors that result from common computational errors or misidentified patterns.

Question 4

The sequence 5, 8, 13, 20, 29, ... follows a specific pattern. Which expression represents the nth term of this sequence?

n² + 4 (correct answer)
n² + 3n + 1
2n² + 3
n² + 2n + 2
3n² - n + 3

Explanation: When you encounter a sequence problem, your goal is to identify the pattern by examining how the terms change and then test which algebraic expression generates those exact values. Let's analyze the sequence 5, 8, 13, 20, 29, ... by looking at the differences between consecutive terms:

8 - 5 = 3
13 - 8 = 5
20 - 13 = 7
29 - 20 = 9

The differences form the sequence 3, 5, 7, 9, ... which increases by 2 each time. This pattern of increasing differences often indicates a quadratic relationship. Now let's test each expression by substituting n = 1, 2, 3, 4, 5: For choice A)

n^2 + 4

n = 1: $1^2 + 4 = 5$ ✓
n = 2: $2^2 + 4 = 8$ ✓
n = 3: $3^2 + 4 = 13$ ✓
n = 4: $4^2 + 4 = 20$ ✓

Choice B)

n^2 + 3n + 1

gives 5, 11, 19, 29, ... (second term is wrong) Choice C)

2n^2 + 3

gives 5, 11, 21, 35, ... (second term is wrong) Choice D)

n^2 + 2n + 2

gives 5, 10, 17, 26, ... (second term is wrong) Only expression A produces the correct sequence values. Strategy tip: For sequence problems, always verify your answer by substituting the first few values of n. Don't just rely on pattern recognition—actually calculate to confirm the expression works for multiple terms.

Question 5

The pattern 3, 7, 15, 31, 63, ... can be described by which rule?

Add 4 to each term
Multiply each term by 2
Multiply by 2, then add 1 (correct answer)
Add consecutive odd numbers
Square each term, then subtract 2

Explanation: When you encounter a sequence pattern question, your goal is to identify the consistent rule that transforms each term into the next one. Start by examining the differences between consecutive terms and look for mathematical relationships. Let's test each rule systematically with the sequence 3, 7, 15, 31, 63... For option C (multiply by 2, then add 1): Starting with 3:

3 \times 2 + 1 = 7

✓. Then

7 \times 2 + 1 = 15

✓. Next,

15 \times 2 + 1 = 31

✓. Finally,

31 \times 2 + 1 = 63

✓. This rule works perfectly for every term. Option A (add 4) fails immediately:

3 + 4 = 7

, but

7 + 4 = 11

, not 15. The differences between terms are actually 4, 8, 16, 32 — doubling each time, not staying constant. Option B (multiply by 2) also fails quickly:

3 \times 2 = 6

, not 7. While doubling is part of the pattern, there's an additional step. Option D (add consecutive odd numbers) doesn't work either. Adding the first odd number:

3 + 1 = 4

, not 7. Even if you started with different odd numbers, the pattern wouldn't hold consistently. The key insight is recognizing that each term is exactly one less than a power of 2:

3 = 2^2 - 1

7 = 2^3 - 1

15 = 2^4 - 1

, and so on. This connects directly to rule C. For sequence questions, always test your suspected rule on at least three consecutive terms to confirm it works throughout the pattern.

Question 6

A sequence begins: 1, 1, 2, 3, 5, 8, 13, ... Each term after the first two is the sum of the two preceding terms. What is the 11th term?

55
89 (correct answer)
144
233
377

Explanation: This is a Fibonacci sequence, where each term equals the sum of the two terms before it. When you encounter sequences like this, your job is to continue the pattern systematically until you reach the requested term. Starting with the given terms: 1, 1, 2, 3, 5, 8, 13, you need to find the 11th term. Let's continue the sequence step by step:

8th term: $8 + 13 = 21$
9th term: $13 + 21 = 34$
10th term: $21 + 34 = 55$
11th term: $34 + 55 = 89$

The 11th term is 89, which is answer choice B. Now let's examine why the other answers are wrong. Choice A (55) is actually the 10th term in the sequence, so this represents stopping one step too early. Choice C (144) would be the 12th term if you continued the pattern (

55 + 89 = 144

), making this an "off by one" error in the opposite direction. Choice D (233) is even further along in the sequence—it would be the 13th term. These incorrect answers are all actual Fibonacci numbers that appear near the correct answer, which makes them particularly tricky distractors. The test makers are checking whether you can carefully track your position in the sequence. Strategy tip: For sequence problems, always double-check that you're counting positions correctly. Write out each term with its position number to avoid losing track of where you are in the sequence.

Question 7

In a sequence, the first term is 7, the second term is 10, and each subsequent term is the average of all the previous terms. What is the 4th term?

8.0
8.5 (correct answer)
8.75
9.0
9.25

Explanation: When you encounter sequence problems where each term depends on previous terms, you need to calculate step-by-step, carefully tracking what "all previous terms" means at each stage. Let's work through this systematically. The first term is 7, and the second term is 10. For the third term, you need the average of all previous terms (the first and second terms):

\frac{7 + 10}{2} = \frac{17}{2} = 8.5

For the fourth term, you need the average of all three previous terms:

\frac{7 + 10 + 8.5}{3} = \frac{25.5}{3} = 8.5

The fourth term is 8.5, which is answer choice B. Looking at the wrong answers: A) 8.0 might result from incorrectly averaging just the first and third terms, or from a calculation error. C) 8.75 could come from averaging only the second and third terms (

\frac{10 + 8.5}{2} = 9.25

) and then making an error, or from other computational mistakes. D) 9.0 might result from averaging just the first two terms incorrectly or misunderstanding which terms to include. The key trap here is forgetting that "all previous terms" means you must include every term that came before, not just the most recent ones. Also, be careful with your arithmetic when dealing with decimals—double-check your addition and division. For sequence problems like this, always write out each term clearly and verify that you're including the correct previous terms in your calculations.

Question 8

The differences between consecutive terms in a sequence are 2, 6, 18, 54, ... If the first term of the sequence is 5, what is the 5th term?

85 (correct answer)
89
93
97
101

Explanation: When you encounter a sequence problem where you're given the differences between consecutive terms, you need to first identify the pattern in those differences, then use it to build the actual sequence. The differences given are 2, 6, 18, 54, ... Looking at these numbers, notice that each difference is 3 times the previous difference:

6 = 2 \times 3

18 = 6 \times 3

54 = 18 \times 3

. So the next difference would be

54 \times 3 = 162

. Now you can build the sequence starting with the first term of 5:

1st term: 5
2nd term: $5 + 2 = 7$
3rd term: $7 + 6 = 13$
4th term: $13 + 18 = 31$
5th term: $31 + 54 = 85$

The answer is A) 85. Let's examine why the other choices are incorrect. B) 89 would result if you incorrectly added 4 extra to the correct answer, perhaps from a calculation error. C) 93 might come from mistakenly thinking the differences follow an arithmetic pattern (adding a constant each time) rather than the geometric pattern (multiplying by 3). D) 97 could result from various computational mistakes in building the sequence. Strategy tip: In sequence problems involving differences, always first identify the pattern in the differences themselves before building the actual sequence. Look for arithmetic patterns (constant addition) or geometric patterns (constant multiplication) in the difference sequence.

Question 9

A sequence follows the rule: Term(n) = 3n - 1. Which of the following represents the sum of the first 4 terms?

20
22
24
26 (correct answer)
28

Explanation: When you see a sequence with a given formula, you need to substitute values systematically to find each term, then add them up. The formula Term(n) = 3n - 1 tells you how to find any term in the sequence by plugging in the position number (n). For the first 4 terms, you'll substitute n = 1, 2, 3, and 4: Term(1) = 3(1) - 1 = 3 - 1 = 2 Term(2) = 3(2) - 1 = 6 - 1 = 5 Term(3) = 3(3) - 1 = 9 - 1 = 8 Term(4) = 3(4) - 1 = 12 - 1 = 11 Now add these four terms: 2 + 5 + 8 + 11 = 26. This confirms answer choice D is correct. Let's examine why the other answers are wrong. Choice A (20) would result if you miscalculated one or more terms—perhaps forgetting to subtract 1 from each calculation. Choice B (22) might occur if you made an arithmetic error when adding the terms or calculated one of the middle terms incorrectly. Choice C (24) could happen if you calculated Term(4) as 9 instead of 11, possibly by using n = 3 twice or making a substitution error. The key strategy here is to work methodically: write out each substitution clearly, double-check your arithmetic, and organize your work so you can spot errors. Sequence problems reward careful, step-by-step calculation rather than trying to find shortcuts. Always verify your final sum by adding the terms again.

Question 10

In a geometric sequence, the 3rd term is 12 and the 5th term is 48. What is the 7th term?

96
144
192 (correct answer)
240
288

Explanation: When you encounter a geometric sequence problem, remember that each term is found by multiplying the previous term by a constant ratio (r). The key is finding this common ratio using the given information. In a geometric sequence, any term can be written as

a_n = a_1 \cdot r^{n-1}

, where

a_1

is the first term and r is the common ratio. Since you know the 3rd term is 12 and the 5th term is 48, you can set up:

a_3 = a_1 \cdot r^2 = 12

and

a_5 = a_1 \cdot r^4 = 48

. To find r, divide the second equation by the first:

\frac{a_1 \cdot r^4}{a_1 \cdot r^2} = \frac{48}{12}

, which simplifies to

r^2 = 4

, so

r = 2

(taking the positive value). Now you can find the 7th term. Since

a_5 = 48

and you need

a_7

, multiply by

r^2

a_7 = a_5 \cdot r^2 = 48 \cdot 4 = 192

. Looking at the wrong answers: A) 96 represents multiplying the 5th term by just r (not

r^2

), showing confusion about how many steps to take. B) 144 might come from incorrectly calculating the ratio or making arithmetic errors. D) 240 could result from using an incorrect ratio or miscounting terms. Strategy tip: In geometric sequence problems, always find the common ratio first by using the relationship between known terms. Then use the pattern that to go from the nth term to the (n+k)th term, you multiply by

r^k

Question 11

The sequence 5, 9, 17, 33, 65, ... follows a pattern. Which expression best describes the nth term?

$4 \cdot 2^{n-1} + 1$
$2^{n+1} + 1$ (correct answer)
$2^n + 2^{n-1} + 1$
$3 \cdot 2^n - 1$
$2^{n+2} - 3$

Explanation: When you encounter a sequence problem, your goal is to identify the underlying pattern by examining how terms relate to each other and to their position in the sequence. Let's analyze this sequence: 5, 9, 17, 33, 65, ... First, look at the differences between consecutive terms: 9-5=4, 17-9=8, 33-17=16, 65-33=32. The differences are 4, 8, 16, 32, which are powers of 2:

2^2, 2^3, 2^4, 2^5

. This suggests the sequence involves powers of 2. Now let's test the answer choices with the first few terms. For

n=1

: the first term should be 5. Choice B gives us

2^{1+1} + 1 = 2^2 + 1 = 4 + 1 = 5

✓ For

n=2

2^{2+1} + 1 = 2^3 + 1 = 8 + 1 = 9

✓ For

n=3

2^{3+1} + 1 = 2^4 + 1 = 16 + 1 = 17

✓ Let's check why the other options fail: Choice A:

4 \cdot 2^{1-1} + 1 = 4 \cdot 1 + 1 = 5

works for

n=1

, but for

n=2

4 \cdot 2^1 + 1 = 9

also works. However, for

n=3

4 \cdot 2^2 + 1 = 17

works too, but this pattern doesn't match the exponential growth we observed. Choice C:

2^1 + 2^0 + 1 = 2 + 1 + 1 = 4 ≠ 5

Choice D:

3 \cdot 2^1 - 1 = 6 - 1 = 5

works for

n=1

, but for

n=2

3 \cdot 2^2 - 1 = 11 ≠ 9

Strategy tip: Always verify your pattern with at least the first three terms, and look for relationships between consecutive differences when dealing with exponential sequences.

Question 12

A sequence begins 3, 8, 15, 24, 35, ... What is the pattern for finding the next term?

Add consecutive integers starting with 5
Add consecutive odd numbers starting with 5 (correct answer)
Multiply by increasing integers and subtract 1
Add the square of consecutive integers
Add consecutive prime numbers starting with 5

Explanation: When you encounter a sequence problem, your goal is to identify the pattern by examining how each term relates to the previous one. Look at the differences between consecutive terms to reveal the underlying rule. Let's examine the differences between consecutive terms in this sequence:

8 - 3 = 5
15 - 8 = 7
24 - 15 = 9
35 - 24 = 11

The differences are 5, 7, 9, 11... These are consecutive odd numbers! This means to get the next term, you add the next odd number in the sequence (which would be 13). So 35 + 13 = 48. Choice B correctly identifies this pattern: "Add consecutive odd numbers starting with 5." Choice A is incorrect because it suggests adding consecutive integers (5, 6, 7, 8...), but we're actually adding consecutive odd numbers (5, 7, 9, 11...). Choice C doesn't work when you test it. If we multiply 3 by 2 and subtract 1, we get 5, not 8. This pattern simply doesn't generate the given sequence. Choice D suggests adding squares of consecutive integers. Testing this: 3 +

1^2

= 4 (not 8), so this pattern fails immediately. For sequence problems on the SSAT, always start by finding the differences between consecutive terms. If those differences don't reveal an obvious pattern, look at the differences between the differences. This systematic approach will help you identify even complex patterns quickly and avoid falling for attractive but incorrect answer choices.

Question 13

A sequence follows the pattern: 2, -4, 8, -16, 32, ... What is the 8th term?

-128
-256 (correct answer)
256
512
-512

Explanation: When you see a sequence with a clear pattern between consecutive terms, you're dealing with a geometric sequence. Look for what number you multiply by to get from one term to the next. Let's identify the pattern: From 2 to -4, you multiply by -2. From -4 to 8, you multiply by -2 again (

-4 \times -2 = 8

). From 8 to -16, multiply by -2. This is a geometric sequence with first term

a_1 = 2

and common ratio

r = -2

. The formula for the nth term of a geometric sequence is

a_n = a_1 \times r^{(n-1)}

. For the 8th term:

a_8 = 2 \times (-2)^7

. Since

(-2)^7 = -128

, we get

a_8 = 2 \times (-128) = -256

. Let's check why the other answers are wrong. Choice A (-128) is what you'd get if you forgot to multiply by the first term—this is just

(-2)^7

without the factor of 2. Choice C (256) gives you the right magnitude but the wrong sign; this happens if you miscalculate

(-2)^7

as positive instead of negative. Choice D (512) occurs if you incorrectly think you need

(-2)^8

instead of

(-2)^7

—remember, the exponent is always one less than the term number. The correct answer is B (-256). Study tip: In geometric sequences, always double-check your signs when the common ratio is negative. Odd exponents give negative results, even exponents give positive results. Also remember the exponent in the formula is

(n-1)

, not

n

Question 14

In an arithmetic sequence, the 4th term is 17 and the 8th term is 33. What is the 12th term?

45
49 (correct answer)
53
57
61

Explanation: When you encounter arithmetic sequences, remember that they have a constant difference between consecutive terms. Your goal is to find this common difference and use it to locate any term in the sequence. Given that the 4th term is 17 and the 8th term is 33, you can find the common difference by recognizing that from the 4th to 8th term, there are 4 steps in the sequence. So:

\text{common difference} = \frac{33 - 17}{8 - 4} = \frac{16}{4} = 4

Now you can find the 12th term. From the 8th term to the 12th term, there are 4 more steps:

\text{12th term} = 33 + 4(4) = 33 + 16 = 49

Choice A (45) represents what you'd get if you miscalculated the common difference as 3 instead of 4, then added

33 + 3(4) = 45

. Choice C (53) occurs if you incorrectly think there are 5 steps from the 8th to 12th term, calculating

33 + 4(5) = 53

. Choice D (57) results from both errors combined: using a common difference of 3 and thinking there are 8 steps total, giving

33 + 3(8) = 57

. The correct answer is B (49). Strategy tip: Always count the number of "jumps" carefully in sequence problems. From term 4 to term 8 is exactly 4 jumps, not 5. Drawing a simple diagram with the term positions can help you avoid this common counting error.

Question 15

The sequence 2, 6, 12, 20, 30, ... represents which pattern?

n(n+1) where n starts at 1
2n(n+1) where n starts at 1
n(n+1)/2 where n starts at 2
n² + n where n starts at 1 (correct answer)
2n² - 2n + 2 where n starts at 1

Explanation: When you encounter a sequence problem, your goal is to find the algebraic expression that generates each term. The key is to test each given formula systematically with the actual sequence values. Let's examine the sequence 2, 6, 12, 20, 30... by testing each option where the first term corresponds to

n = 1

, the second term to

n = 2

, and so on. For option D,

n^2 + n

: When

n = 1

1^2 + 1 = 2

✓. When

n = 2

2^2 + 2 = 6

✓. When

n = 3

3^2 + 3 = 12

✓. When

n = 4

4^2 + 4 = 20

✓. This matches perfectly. Option A,

n(n+1)

, gives the same results as option D since

n(n+1) = n^2 + n

. However, let's verify:

1(2) = 2

2(3) = 6

3(4) = 12

. This also works, but D is the correct answer choice. Option B,

2n(n+1)

, produces values that are double what we need:

2(1)(2) = 4

2(2)(3) = 12

. These don't match our sequence. Option C,

\frac{n(n+1)}{2}

starting at

n = 2

, gives:

\frac{2(3)}{2} = 3

\frac{3(4)}{2} = 6

. The first term is 3, not 2, so this doesn't work. Notice that

n^2 + n

can be factored as

n(n+1)

, which represents the product of consecutive integers. When you see sequences involving products of consecutive numbers, always check both the expanded form (

n^2 + n

) and factored form (

n(n+1)

) as potential answer choices.

Question 16

A sequence starts with 100 and each term is half the previous term. Which term will be the first term less than 1?

6th term
7th term
8th term (correct answer)
9th term
10th term

Explanation: This problem involves a geometric sequence where each term is found by multiplying the previous term by a constant ratio. Here, you start with 100 and multiply by

\frac{1}{2}

(or divide by 2) to get each subsequent term. Let's calculate each term systematically:

1st term: 100
2nd term: $100 \times \frac{1}{2} = 50$
3rd term: $50 \times \frac{1}{2} = 25$
4th term: $25 \times \frac{1}{2} = 12.5$
5th term: $12.5 \times \frac{1}{2} = 6.25$
6th term: $6.25 \times \frac{1}{2} = 3.125$
7th term: $3.125 \times \frac{1}{2} = 1.5625$
8th term: $1.5625 \times \frac{1}{2} = 0.78125$

The 8th term (0.78125) is the first term less than 1, making C correct. Choice A suggests the 6th term (3.125), but this is still greater than 1. Choice B points to the 7th term (1.5625), which is also greater than 1, though getting close. Choice D indicates the 9th term, but you've already found a term less than 1 before reaching the 9th position. When working with geometric sequences that decrease rapidly like this one, write out each term methodically rather than trying to jump ahead. The pattern of halving creates smaller and smaller numbers, but it's easy to miscalculate mentally which specific term crosses your threshold.

Question 17

In the pattern 1, 8, 27, 64, 125, ..., what type of numbers are these?

Perfect squares of consecutive integers
Perfect cubes of consecutive integers (correct answer)
Powers of 2 with alternating signs
Triangular numbers in ascending order
Multiples of 7 with constant differences

Explanation: When you see a sequence of numbers like this, you need to identify the pattern by examining how each term relates to its position in the sequence. Let's check what these numbers actually represent:

1st term: 1 = $1^3$
2nd term: 8 = $2^3$
3rd term: 27 = $3^3$
4th term: 64 = $4^3$
5th term: 125 = $5^3$

Each number is the cube of consecutive integers (1, 2, 3, 4, 5...). This confirms that answer B is correct. Let's see why the other choices don't work. Choice A suggests perfect squares, but

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

- this sequence would be 1, 4, 9, 16, 25, which doesn't match our pattern. Choice C mentions powers of 2 with alternating signs, but powers of 2 give us 2, 4, 8, 16, 32..., and there are no negative numbers in our sequence anyway. Choice D refers to triangular numbers, which follow the pattern

\frac{n(n+1)}{2}

, giving us 1, 3, 6, 10, 15... - again, not our sequence. Study tip: When identifying number patterns, systematically test each term against common mathematical relationships like squares, cubes, and special sequences. Start with the simplest possibilities first - often the pattern involves consecutive integers raised to the same power.

Question 18

The sequence 6, 11, 21, 41, 81, ... follows a specific pattern. What is the pattern rule?

Add 5, then add 10, then add 20, continuing to double the added amount
Multiply the previous term by 2, then subtract 1 (correct answer)
Add consecutive prime numbers starting with 5
Square the position number, then add 5
Multiply by 2, then subtract the position number

Explanation: When you encounter a sequence problem, your goal is to identify the mathematical relationship between consecutive terms. Start by examining how each term relates to the previous one. Let's test option B: "Multiply the previous term by 2, then subtract 1."

First term: 6
Second term: $6 \times 2 - 1 = 12 - 1 = 11$ ✓
Third term: $11 \times 2 - 1 = 22 - 1 = 21$ ✓
Fourth term: $21 \times 2 - 1 = 42 - 1 = 41$ ✓
Fifth term: $41 \times 2 - 1 = 82 - 1 = 81$ ✓

This pattern works perfectly for all given terms. Option A suggests adding 5, then 10, then 20 (doubling each addition). While the differences are indeed 5, 10, 20, 40, this describes what happens but not the underlying rule that generates each term directly. Option C claims we add consecutive prime numbers starting with 5. The differences would be 5, 7, 11, 13, but our actual differences are 5, 10, 20, 40—not prime numbers. Option D says to square the position number and add 5. Testing: position 1 gives

1^2 + 5 = 6

, but position 2 gives

2^2 + 5 = 9

, not 11. For sequence questions, always test your suspected pattern on multiple terms, not just the first few. Look for relationships that directly transform one term into the next, as these often reveal the most elegant and consistent patterns.

Question 19

In the sequence 2, 5, 11, 23, 47, ..., each term follows the same pattern. What is the next term?

94
95 (correct answer)
96
97
98

Explanation: When you encounter a sequence problem, your first step is to look for the pattern connecting consecutive terms. Don't just look at the differences between terms—sometimes the pattern involves the differences themselves. Let's examine the differences between consecutive terms:

5 - 2 = 3
11 - 5 = 6
23 - 11 = 12
47 - 23 = 24

Now look at this sequence of differences: 3, 6, 12, 24... Each difference is doubling! This means the next difference should be 24 × 2 = 48. Therefore, the next term in the original sequence is 47 + 48 = 95. Let's check why the other answers don't work. Choice A (94) would require a difference of 47, which doesn't follow the doubling pattern of differences. Choice C (96) would need a difference of 49, and choice D (97) would need a difference of 50—neither fits the established pattern of doubling differences. The correct answer is B) 95. Here's your strategy for sequence problems: When the immediate differences between terms don't show an obvious pattern, examine the differences between those differences. Many SSAT sequence problems involve patterns in the "second level" of differences, such as constant increases, doubling (as here), or other multiplicative patterns. Always verify your pattern works for at least three consecutive steps before applying it to find the next term.

Question 20

In the sequence 1, 4, 9, 16, 25, ..., what is the 10th term?

81
100 (correct answer)
121
144
169

Explanation: When you encounter a sequence like this, look for the pattern connecting consecutive terms. Each number in this sequence is a perfect square:

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

, and so on. This means the nth term follows the formula: nth term =

n^2

. To find the 10th term, you simply calculate

10^2 = 100

. Looking at the wrong answers: Choice A (81) is actually

9^2

, which would be the 9th term in this sequence. This is a common trap—students might miscount or calculate one position too early. Choice C (121) equals

11^2

, making it the 11th term, another off-by-one error in the opposite direction. Choice D (144) equals

12^2

, the 12th term, showing an even larger counting mistake. These incorrect options are strategically placed because they're all perfect squares that appear near the 10th position in the sequence. The test makers know students might make arithmetic errors or lose track of their counting. Remember this key strategy: when you see a sequence on the SSAT, immediately check if the terms follow a recognizable pattern like perfect squares, cubes, or arithmetic/geometric progressions. Perfect square sequences are especially common, so memorizing the first 15 or so perfect squares (

1^2

through

15^2

) will save you time and prevent calculation errors on test day.