SSAT Middle Level Quantitative Quiz: Pattern Rules From Sequences
20 questions · exam conditions
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Pattern Rules From SequencesQuestion 1 of 20

Explain how the sequence is formed: 30,27,24,21,1830, 27, 24, 21, 18.

Subtract 3 each time
Add 3 each time
Multiply by 3 each time
Subtract 6 each time
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SSAT Middle Level Quantitative Quiz

SSAT Middle Level Quantitative Quiz: Pattern Rules From Sequences

Practice Pattern Rules From Sequences in SSAT Middle Level Quantitative 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 Quantitative.

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

Explain how the sequence is formed: 30,27,24,21,1830, 27, 24, 21, 18.

  1. Subtract 3 each time (correct answer)
  2. Add 3 each time
  3. Multiply by 3 each time
  4. Subtract 6 each time
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 decreased by 3 to produce the next. Choice A is correct because it accurately describes the sequence's rule, showing understanding of arithmetic progression with a negative common difference. Choice B is incorrect because it suggests adding 3, reflecting a common misconception of reversing the direction of change. 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

What operation is used to generate 81,27,9,3,181, 27, 9, 3, 1?

  1. Divide by 3 each time (correct answer)
  2. Subtract 3 each time
  3. Add 3 each time
  4. Multiply by 3 each time
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 3 to produce the next. Choice A is correct because it accurately describes the sequence's rule, showing understanding of geometric progression with a common ratio of 1/3. Choice D is incorrect because it suggests multiplying by 3, reflecting a common misconception of inverting the operation. 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

What is the rule for 2,6,18,54,1622, 6, 18, 54, 162?

  1. Add 4 each time
  2. Multiply by 2 each time
  3. Multiply by 3 each time (correct answer)
  4. Add 6 each time
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 3 to produce the next. Choice C is correct because it accurately describes the sequence's rule, showing understanding of geometric progression with a common ratio of 3. Choice B is incorrect because it suggests multiplying by 2, reflecting a common misconception of underestimating the ratio. 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 4

What is the rule for 8,12,18,27,40,608, 12, 18, 27, 40, 60?

  1. Add 4, 6, 9, 13, 20 (correct answer)
  2. Multiply by 2 each time
  3. Add 4 each time
  4. Subtract 4 each time
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, the differences are 4, 6, 9, 13, 20, which may follow an approximate multiplication by 1.5 with adjustments. Choice A is correct because it accurately lists the additions that generate the sequence, showing understanding of variable differences. Choice B is incorrect because it suggests multiplying by 2 each time, reflecting a common misconception of assuming a geometric progression. 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 5

What operation is used to generate 7,14,28,56,1127, 14, 28, 56, 112?

  1. Add 7 each time
  2. Multiply by 2 each time (correct answer)
  3. Multiply by 3 each time
  4. Subtract 7 each time
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 B is correct because it accurately describes the sequence's rule, showing understanding of geometric progression with a common ratio of 2. Choice A is incorrect because it suggests adding 7, reflecting a common misconception of mistaking multiplication for addition. 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 6

Identify the pattern rule for 13,26,52,104,20813, 26, 52, 104, 208.

  1. Add 13 each time
  2. Multiply by 3 each time
  3. Multiply by 2 each time (correct answer)
  4. Add 26 each time
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 describes the sequence's rule, showing understanding of geometric progression with a common ratio of 2. Choice A is incorrect because it suggests adding 13, reflecting a common misconception of confusing addition with multiplication. 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 7

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

  1. 81
  2. 90
  3. 144 (correct answer)
  4. 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 8

Which sequence follows the same rule as 5,10,15,20,255, 10, 15, 20, 25?

  1. 2,4,8,16,322, 4, 8, 16, 32
  2. 7,12,17,22,277, 12, 17, 22, 27 (correct answer)
  3. 9,11,14,18,239, 11, 14, 18, 23
  4. 30,25,20,15,1030, 25, 20, 15, 10
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, numbers increase by 5 each time, and choice B follows the same arithmetic rule. Choice B is correct because it accurately matches the rule of adding 5, showing understanding of consistent arithmetic progressions. Choice A is incorrect because it uses multiplication by 2, reflecting a common misconception of applying geometric rules to arithmetic sequences. 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 9

What operation is used to generate 3,6,12,24,483, 6, 12, 24, 48?

  1. Add 3 each time
  2. Multiply by 2 each time (correct answer)
  3. Subtract 3 each time
  4. Multiply by 3 each time
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 B is correct because it accurately describes the sequence's rule, showing understanding of geometric progression with a common ratio of 2. Choice A is incorrect because it suggests adding 3 each time, reflecting a common misconception of confusing multiplication with addition. 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 10

Explain how the sequence is formed: 20,18,21,19,22,2020, 18, 21, 19, 22, 20.

  1. Subtract 2, then add 3 (correct answer)
  2. Add 2, then subtract 3
  3. Add 1 each time
  4. Multiply by 2 each time
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, the pattern alternates between subtracting 2 and adding 3. Choice A is correct because it accurately describes the sequence's rule, showing understanding of alternating operations. Choice B is incorrect because it reverses the operations, reflecting a common misconception of misordering the pattern. 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 11

Identify the pattern in 2,5,10,17,26,372, 5, 10, 17, 26, 37.

  1. Add 3 each time
  2. Add 3, 5, 7, 9, 11 (correct answer)
  3. Multiply by 2 each time
  4. Add 4, then add 6 repeatedly
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, the differences increase by 2 each time, starting with adding 3, then 5, 7, 9, 11. Choice B is correct because it accurately describes the sequence's rule, showing understanding of increasing arithmetic differences. Choice A is incorrect because it suggests adding 3 constantly, reflecting a common misconception of ignoring the changing differences. 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 12

What is the rule for 6,11,16,21,266, 11, 16, 21, 26?

  1. Add 4 each time
  2. Add 5 each time (correct answer)
  3. Multiply by 5 each time
  4. Subtract 5 each time
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 increased by 5 to produce the next. Choice B is correct because it accurately describes the sequence's rule, showing understanding of arithmetic progression with a common difference of 5. Choice A is incorrect because it suggests adding 4, reflecting a common misconception of undercalculating the difference. 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 13

Identify the pattern in 5,8,6,9,7,105, 8, 6, 9, 7, 10.

  1. Add 3 each time
  2. Add 3, then subtract 2 (correct answer)
  3. Subtract 3, then add 2
  4. Add 1 each time
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, the pattern alternates between adding 3 and subtracting 2. Choice B is correct because it accurately describes the sequence's rule, showing understanding of alternating operations in a pattern. Choice D is incorrect because it suggests adding 1 each time, reflecting a common misconception of averaging the net change. 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 14

Identify the pattern rule for 4,9,14,19,24,294, 9, 14, 19, 24, 29.

  1. Add 4 each time
  2. Multiply by 2 each time
  3. Add 5 each time (correct answer)
  4. Add 5, then add 4
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 increased by 5 to produce the next. Choice C is correct because it accurately describes the sequence's rule, showing understanding of arithmetic progression with a common difference of 5. Choice A is incorrect because it suggests adding 4 each time, reflecting a common misconception of miscalculating the constant difference. 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 15

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

  1. 3
  2. 2 (correct answer)
  3. 1
  4. 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 16

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?

  1. 108
  2. 162 (correct answer)
  3. 216
  4. 270
  5. 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=36 ÷ 2 = 3, 18÷6=318 ÷ 6 = 3, and 54÷18=354 ÷ 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=16254 × 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=36 ÷ 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 17

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

  1. n² + 4 (correct answer)
  2. n² + 3n + 1
  3. 2n² + 3
  4. n² + 2n + 2
  5. 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) n2+4n^2 + 4:
  • n = 1: 12+4=51^2 + 4 = 5 ✓
  • n = 2: 22+4=82^2 + 4 = 8 ✓
  • n = 3: 32+4=133^2 + 4 = 13 ✓
  • n = 4: 42+4=204^2 + 4 = 20 ✓
Choice B) n2+3n+1n^2 + 3n + 1 gives 5, 11, 19, 29, ... (second term is wrong) Choice C) 2n2+32n^2 + 3 gives 5, 11, 21, 35, ... (second term is wrong) Choice D) n2+2n+2n^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 18

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

  1. Add 4 to each term
  2. Multiply each term by 2
  3. Multiply by 2, then add 1 (correct answer)
  4. Add consecutive odd numbers
  5. 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: 3×2+1=73 \times 2 + 1 = 7 ✓. Then 7×2+1=157 \times 2 + 1 = 15 ✓. Next, 15×2+1=3115 \times 2 + 1 = 31 ✓. Finally, 31×2+1=6331 \times 2 + 1 = 63 ✓. This rule works perfectly for every term. Option A (add 4) fails immediately: 3+4=73 + 4 = 7, but 7+4=117 + 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: 3×2=63 \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=43 + 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=22−13 = 2^2 - 1, 7=23−17 = 2^3 - 1, 15=24−115 = 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 19

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?

  1. 55
  2. 89 (correct answer)
  3. 144
  4. 233
  5. 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=218 + 13 = 21
  • 9th term: 13+21=3413 + 21 = 34
  • 10th term: 21+34=5521 + 34 = 55
  • 11th term: 34+55=8934 + 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=14455 + 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 20

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?

  1. 8.0
  2. 8.5 (correct answer)
  3. 8.75
  4. 9.0
  5. 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): 7+102=172=8.5\frac{7 + 10}{2} = \frac{17}{2} = 8.5 For the fourth term, you need the average of all three previous terms: 7+10+8.53=25.53=8.5\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 (10+8.52=9.25\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.