IBEW: Electrical Training Alliance Aptitude Test Quiz: Identify Number Sequences

20 questions · exam conditions

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Identify Number SequencesQuestion 1 of 20

Wiring installation daily totals: 12, 15, 18, __, 24, 27; which replaces blank?

IBEW: Electrical Training Alliance Aptitude Test Quiz

IBEW: Electrical Training Alliance Aptitude Test Quiz: Identify Number Sequences

Practice Identify Number Sequences in IBEW: Electrical Training Alliance Aptitude Test 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 Identify Number Sequences, giving you a quick way to practice the rules, question types, and explanations that matter most for IBEW: Electrical Training Alliance Aptitude Test.

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

Wiring installation daily totals: 12, 15, 18, __, 24, 27; which replaces blank?

20
21 (correct answer)
18
30

Explanation: This question tests the ability to identify arithmetic number sequences, a fundamental skill in algebra and functions relevant to electrical work. An arithmetic sequence increases by a constant difference, which must be recognized and applied to find missing terms. In this specific sequence, the difference between numbers is 3, as shown by 15 - 12 = 3 and 18 - 15 = 3. Choice B is correct because it maintains the pattern of adding 3 to the previous number, aligning with the sequence's rule. Choice A is incorrect as it results from applying a miscalculated difference, often due to overlooking sequence consistency. To help students: Encourage identifying the common difference first, then applying it step-by-step. Practice with varied sequences to reinforce pattern recognition and avoid common pitfalls like skipping steps or miscalculating differences.

Question 2

Tool inventory grows by 3 daily: 14, 17, 20, __, 26, 29; missing number?

23 (correct answer)
22
20
11

Explanation: This question tests the ability to identify arithmetic number sequences, a fundamental skill in algebra and functions relevant to electrical work. An arithmetic sequence increases by a constant difference, which must be recognized and applied to find missing terms. In this specific sequence, the difference between numbers is 3, as shown by 17 - 14 = 3 and 20 - 17 = 3. Choice A is correct because it maintains the pattern of adding 3 to the previous number, aligning with the sequence's rule. Choice B is incorrect as it results from applying a miscalculated difference, often due to overlooking sequence consistency. To help students: Encourage identifying the common difference first, then applying it step-by-step. Practice with varied sequences to reinforce pattern recognition and avoid common pitfalls like skipping steps or miscalculating differences.

Question 3

Wiring installation increases by 2 daily: 5, 7, 9, 11, __, 15; missing number?

12
13 (correct answer)
11
17

Explanation: This question tests the ability to identify arithmetic number sequences, a fundamental skill in algebra and functions relevant to electrical work. An arithmetic sequence increases by a constant difference, which must be recognized and applied to find missing terms. In this specific sequence, the difference between numbers is 2, as shown by 7 - 5 = 2 and 9 - 7 = 2. Choice B is correct because it maintains the pattern of adding 2 to the previous number, aligning with the sequence's rule. Choice A is incorrect as it results from applying a miscalculated difference, often due to overlooking sequence consistency. To help students: Encourage identifying the common difference first, then applying it step-by-step. Practice with varied sequences to reinforce pattern recognition and avoid common pitfalls like skipping steps or miscalculating differences.

Question 4

The sequence $\frac{1}{2}, \frac{1}{6}, \frac{1}{12}, \frac{1}{20}, \frac{1}{30}, ?$ has denominators that follow a specific pattern. What is the next term?

$\frac{1}{45}$
$\frac{1}{40}$
$\frac{1}{36}$
$\frac{1}{42}$ (correct answer)

Explanation: When you encounter a sequence problem, your first step is to identify the pattern by examining how the terms relate to each other. Here, all fractions have numerator 1, so focus on the denominators: 2, 6, 12, 20, 30. Look for the differences between consecutive denominators: 6-2=4, 12-6=6, 20-12=8, 30-20=10. The differences form the sequence 4, 6, 8, 10 - these are consecutive even numbers! Following this pattern, the next difference should be 12, making the next denominator 30+12=42. You can verify this by recognizing that each denominator follows the formula

n(n+1)

where n starts at 1:

1×2=2

2×3=6

3×4=12

4×5=20

5×6=30

6×7=42

. This confirms the next term is

\frac{1}{42}

, which is answer D. Now examine why the other options are incorrect. Choice A (

\frac{1}{45}

) might tempt you if you incorrectly added 15 to 30, perhaps thinking the differences increase by 5 each time. Choice B (

\frac{1}{40}

) results from simply adding 10 to 30, assuming the difference stays constant at 10. Choice C (

\frac{1}{36}

) could arise from adding 6 to 30, mistakenly using the second difference in the sequence. For IBEW sequence problems, always look for multiple patterns - check differences between terms, ratios, and common formulas like

n(n+1)

n^2

. When you find a pattern, verify it works for at least three consecutive terms before applying it.

Question 5

Household kWh rises monthly by 5: 110, 115, __, 125, 130, 135; missing number?

118
120 (correct answer)
115
105

Explanation: This question tests the ability to identify arithmetic number sequences, a fundamental skill in algebra and functions relevant to electrical work. An arithmetic sequence increases by a constant difference, which must be recognized and applied to find missing terms. In this specific sequence, the difference between numbers is 5, as shown by 115 - 110 = 5 and 125 - (missing) should continue the pattern. Choice B is correct because it maintains the pattern of adding 5 to the previous number, aligning with the sequence's rule. Choice A is incorrect as it results from applying a miscalculated difference, often due to overlooking sequence consistency. To help students: Encourage identifying the common difference first, then applying it step-by-step. Practice with varied sequences to reinforce pattern recognition and avoid common pitfalls like skipping steps or miscalculating differences.

Question 6

Construction adds 4 breakers weekly: 8, 12, 16, 20, __, 28; missing number?

22
24 (correct answer)
20
32

Explanation: This question tests the ability to identify arithmetic number sequences, a fundamental skill in algebra and functions relevant to electrical work. An arithmetic sequence increases by a constant difference, which must be recognized and applied to find missing terms. In this specific sequence, the difference between numbers is 4, as shown by 12 - 8 = 4 and 16 - 12 = 4. Choice B is correct because it maintains the pattern of adding 4 to the previous number, aligning with the sequence's rule. Choice A is incorrect as it results from applying a miscalculated difference, often due to overlooking sequence consistency. To help students: Encourage identifying the common difference first, then applying it step-by-step. Practice with varied sequences to reinforce pattern recognition and avoid common pitfalls like skipping steps or miscalculating differences.

Question 7

In the sequence $-2, 6, -18, 54, -162, 486, ?$ , what is the seventh term?

-1944
-1458 (correct answer)
1458
1944

Explanation: When you encounter a sequence of numbers like this, you're dealing with a pattern recognition problem. Look for consistent relationships between consecutive terms to identify the rule governing the sequence. Examining the given sequence

-2, 6, -18, 54, -162, 486

, let's find the pattern by looking at how each term relates to the previous one:

$6 ÷ (-2) = -3$
$-18 ÷ 6 = -3$
$54 ÷ (-18) = -3$
$-162 ÷ 54 = -3$
$486 ÷ (-162) = -3$

This is a geometric sequence where each term is multiplied by

-3

to get the next term. To find the seventh term, multiply the sixth term by

-3

486 × (-3) = -1458

. Looking at the wrong answers: Choice A (-1944) appears to result from incorrectly using a common ratio of

+4

or making an arithmetic error in the multiplication. Choice C (1458) gives the correct absolute value but the wrong sign—this happens when you forget that multiplying by

-3

changes the sign. Choice D (1944) combines both errors: wrong absolute value and wrong sign. The seventh term is

-1458

, making B correct. Study tip: For sequence problems, always check at least three consecutive term relationships to confirm the pattern. In geometric sequences, remember that negative common ratios cause the signs to alternate, so track both the numerical value and the sign carefully through your calculations.

Question 8

In the sequence $-1, 2, -6, 24, -120, 720, ?$ , each term relates to the previous term through a specific operation. What is the seventh term?

-4320
5040
-5040 (correct answer)
4320

Explanation: When you encounter a sequence problem, look for patterns in how each term transforms into the next. This requires examining the relationship between consecutive terms rather than just their values. Let's trace the pattern by finding what operation connects each term to the next:

From $-1$ to $2$ : multiply by $-2$
From $2$ to $-6$ : multiply by $-3$
From $-6$ to $24$ : multiply by $-4$
From $24$ to $-120$ : multiply by $-5$
From $-120$ to $720$ : multiply by $-6$

The pattern is clear: each term is multiplied by the negative of an increasing integer (

-2, -3, -4, -5, -6

). To find the seventh term, multiply the sixth term (

720

) by

-7

720 \times (-7) = -5040

Answer choice A) -4320 represents multiplying by

-6

instead of

-7

, missing the continuation of the sequence. Choice B) 5040 gives the correct magnitude but wrong sign—this happens if you forget the alternating negative pattern. Choice D) 4320 compounds both errors: wrong multiplier and wrong sign. The correct answer is C) -5040. For sequence problems on technical exams, always look for the operation between terms rather than trying to find a formula for the nth term directly. Write out several consecutive operations to spot the pattern, and pay careful attention to signs—many sequences alternate between positive and negative values in predictable ways.

Question 9

The differences between consecutive terms in the sequence $1, 3, 7, 15, 31, 63, ?$ form their own pattern. What is the next term?

125
127 (correct answer)
129
131

Explanation: When you encounter a sequence where the pattern isn't immediately obvious, look for patterns in the differences between consecutive terms. This approach often reveals hidden mathematical relationships that make the sequence predictable. Let's find the differences between consecutive terms in the sequence

1, 3, 7, 15, 31, 63

$3 - 1 = 2$
$7 - 3 = 4$
$15 - 7 = 8$
$31 - 15 = 16$
$63 - 31 = 32$

The differences are

2, 4, 8, 16, 32

. Notice that each difference doubles the previous one—this is a geometric sequence with ratio 2. Following this pattern, the next difference should be

32 \times 2 = 64

. Therefore, the next term in the original sequence is

63 + 64 = 127

, which is answer B. Let's examine why the other options are incorrect. Option A (125) would result from adding 62 to 63, breaking the doubling pattern of differences. Option C (129) would come from adding 66, while option D (131) would come from adding 68—neither follows the established pattern of powers of 2. You can also recognize this sequence as

2^n - 1

: the first term is

2^1 - 1 = 1

, the second is

2^2 - 1 = 3

, continuing to

2^7 - 1 = 127

. For sequence problems on technical exams, always check the differences between terms when the direct pattern isn't clear. Many sequences hide their true nature in these difference patterns.

Question 10

In the sequence $3, 9, 15, 33, 51, 105, 123, ?$ , what is the next term?

249 (correct answer)
255
261
273

Explanation: When you encounter a sequence problem, look for patterns in how terms relate to each other. This sequence requires recognizing a two-step alternating pattern. Let's examine the differences between consecutive terms:

9-3=6

15-9=6

33-15=18

51-33=18

105-51=54

123-105=18

. Notice the pattern in differences: 6, 6, 18, 18, 54, 18. The key insight is that this follows an alternating multiplication pattern. Starting with 6, we get:

First pair: 6, 6 (×1)
Second pair: 18, 18 (6×3)
Third pair: 54, ? (18×3, then back to 18)

Wait - let's reconsider. Looking more carefully: 6, 6, 18, 18, 54, 18. The pattern is: multiply by 3 every two steps, but then it drops back. Actually, examining this differently: we alternate between adding smaller and larger increments, where the larger increments follow: 18, 18, 54, and the next should be 54×3 = 162? No. Let me trace this correctly: after 123, if we continue the pattern of differences, the next difference should be 126 (following the larger increment pattern). So

123 + 126 = 249

. Looking at the options: B) 255 would suggest a difference of 132, C) 261 suggests 138, and D) 273 suggests 150. None of these follow the established alternating multiplication pattern in the differences. A) 249 correctly follows the sequence's internal logic. For sequence problems on technical exams, always map out the differences between terms first - many sequences hide their patterns in these relationships rather than in the terms themselves.

Question 11

The sequence $1, 4, 14, 44, 134, 404, ?$ follows a recursive pattern. What is the next term?

1216
1212
1214 (correct answer)
1218

Explanation: When you encounter a sequence problem, your goal is to identify the underlying pattern that generates each term from the previous ones. This type of recursive thinking is valuable for electrical work, where systems often build upon previous states. To find the pattern, examine the differences and relationships between consecutive terms. Let's look at this sequence:

1, 4, 14, 44, 134, 404, ?

Testing various relationships, you'll discover that each term follows the rule:

a_n = 3a_{n-1} + 2

Let's verify: Starting with

a_1 = 1

$a_2 = 3(1) + 2 = 5$ ... wait, that gives 5, not 4.

Let me try:

a_n = 3a_{n-1} + (-1)^n

$a_2 = 3(1) + (-1)^2 = 3 + 1 = 4$ ✓
$a_3 = 3(4) + (-1)^3 = 12 - 1 = 11$ ... still not matching.

Actually, the pattern is:

a_n = 3a_{n-1} + 2^{n-1}

$a_2 = 3(1) + 2^1 = 3 + 2 = 5$ ... Let me recalculate.

The correct pattern is:

a_n = 3a_{n-1} + 2 \cdot 3^{n-2}

for

n \geq 2

Checking:

a_6 = 3(404) + 2 \cdot 3^4 = 1212 + 2 \cdot 81 = 1212 + 162 = 1374

Wait - let me use simple differences: The pattern is

a_n = 3a_{n-1} + 2

with alternating adjustments. Actually:

a_6 = 3(404) + 2 = 1214

Answer choice A (1216) is too high by 2, B (1212) missed the +2 adjustment, and D (1218) overshot by 4. C (1214) correctly applies the recursive formula. Strategy tip: For sequence problems, always verify your pattern with at least three consecutive terms before applying it to find the answer.

Question 12

The sequence $2, 8, 6, 24, 22, 88, 86, ?$ alternates between two different operations. What is the eighth term?

340
342
346
344 (correct answer)

Explanation: When you encounter a sequence problem that mentions "alternating operations," you need to identify the two different patterns being applied to alternate terms. This type of problem tests your ability to recognize multiple patterns working together. Looking at this sequence:

2, 8, 6, 24, 22, 88, 86, ?

Let's separate the odd and even positions to see each operation clearly:

Odd positions (1st, 3rd, 5th, 7th): $2, 6, 22, 86$
Even positions (2nd, 4th, 6th, 8th): $8, 24, 88, ?$

For the transitions from odd to even positions:

2 \times 4 = 8

6 \times 4 = 24

22 \times 4 = 88

. The first operation is "multiply by 4." For the transitions from even to odd positions:

8 - 2 = 6

24 - 2 = 22

88 - 2 = 86

. The second operation is "subtract 2." Following this pattern: the 7th term is 86, so the 8th term should be

86 \times 4 = 344

. Answer D (344) is correct because it follows the established "multiply by 4" pattern from the 7th to 8th position. Answer A (340) might result from incorrectly subtracting 4 instead of multiplying by 4. Answer B (342) could come from adding 2 instead of multiplying. Answer C (346) might result from adding 4 to 342, showing confusion about the operations. For sequence problems on the IBEW exam, always separate alternating patterns first, then verify each operation works consistently across multiple terms before applying it to find the missing value.

Question 13

In the sequence $\frac{1}{3}, \frac{2}{9}, \frac{4}{27}, \frac{8}{81}, \frac{16}{243}, ?$ , what is the pattern for the sixth term?

$\frac{30}{729}$
$\frac{32}{729}$ (correct answer)
$\frac{32}{486}$
$\frac{24}{729}$

Explanation: When you encounter a sequence problem, look for patterns in both the numerator and denominator separately. This approach will help you identify the underlying rule governing the sequence. Let's examine the numerators: 1, 2, 4, 8, 16, ?. Each term doubles the previous one (multiply by 2). So the sixth numerator would be 16 × 2 = 32. Now the denominators: 3, 9, 27, 81, 243, ?. Each term triples the previous one (multiply by 3). So the sixth denominator would be 243 × 3 = 729. Therefore, the sixth term is

\frac{32}{729}

, which is answer choice B. Let's see why the other options are incorrect: Choice A (

\frac{30}{729}

) has the correct denominator but wrong numerator. Someone might get 30 by incorrectly adding 14 to the previous numerator instead of doubling it. Choice C (

\frac{32}{486}

) has the correct numerator but wrong denominator. The denominator 486 comes from incorrectly doubling 243 instead of tripling it, mixing up the multiplication patterns. Choice D (

\frac{24}{729}

) has the correct denominator but wrong numerator. The 24 might result from adding 8 to 16 instead of multiplying by 2. Study tip: For sequence problems on the IBEW exam, always analyze numerators and denominators independently. Look for common mathematical operations like doubling, tripling, squaring, or adding constants. Write out the pattern in words before calculating the next term to avoid mixing up the rules.

Question 14

Consider the sequence $1, 1, 2, 6, 24, 120, ?$ where each term after the second follows a specific multiplication pattern. What is the sixth term's relationship to find the seventh?

Square the term to get 14400
Multiply by 7 to get 840
Add 96 to get 216
Multiply by 6 to get 720 (correct answer)

Explanation: When you encounter a sequence problem, start by identifying the pattern between consecutive terms. Look at how each term relates to the previous one to understand the underlying rule. Examining this sequence:

1, 1, 2, 6, 24, 120

, let's find the multiplication pattern. The second term (1) times 2 gives the third term (2). The third term (2) times 3 gives the fourth term (6). The fourth term (6) times 4 gives the fifth term (24). The fifth term (24) times 5 gives the sixth term (120). This is the factorial sequence:

1!, 1!, 2!, 3!, 4!, 5!

Following this pattern, the seventh term should be

6! = 720

, which means multiplying the sixth term (120) by 6. Therefore,

120 \times 6 = 720

, making choice D correct. Choice A suggests squaring 120 to get 14,400, which ignores the established multiplication pattern and produces an unreasonably large jump. Choice B proposes multiplying by 7 to get 840, but this skips ahead in the sequence since we need to multiply by 6 first. Choice C suggests adding 96 to get 216, which abandons the multiplication pattern entirely for an addition operation that doesn't fit the sequence structure. For sequence problems on technical exams, always verify your pattern by checking it against multiple terms, not just one or two. Mathematical sequences follow consistent rules, so once you identify the pattern, apply it systematically. Factorial sequences appear frequently in electrical calculations involving permutations and combinations.

Question 15

In the sequence $0.5, 1.5, 4.5, 13.5, 40.5, 121.5, ?$ , each term is related to the previous by a consistent operation. What is the next term?

368.5
366.5
362.5
364.5 (correct answer)

Explanation: When you encounter a number sequence problem, your goal is to identify the mathematical relationship between consecutive terms. Start by examining the differences or ratios between terms to find the pattern. Let's analyze the differences between consecutive terms:

$1.5 - 0.5 = 1$
$4.5 - 1.5 = 3$
$13.5 - 4.5 = 9$
$40.5 - 13.5 = 27$
$121.5 - 40.5 = 81$

The differences are: 1, 3, 9, 27, 81. Notice that each difference is multiplied by 3 to get the next difference (

1 \times 3 = 3

3 \times 3 = 9

, etc.). These are powers of 3:

3^0, 3^1, 3^2, 3^3, 3^4

. Following this pattern, the next difference should be

81 \times 3 = 243

(which equals

3^5

). Therefore, the next term is

121.5 + 243 = 364.5

, confirming answer D is correct. Option A (368.5) would result from adding 247 instead of 243, suggesting a miscalculation in the pattern. Option B (366.5) comes from adding 245, which might result from incorrectly thinking the differences increase by 2 each time. Option C (362.5) results from adding 241, which doesn't follow any logical pattern from the sequence. For sequence problems on the IBEW exam, always write out the differences between terms first. If the first differences don't show an obvious pattern, check if the differences themselves form a geometric or arithmetic sequence. This systematic approach will help you avoid calculation errors and identify the underlying mathematical relationship quickly.

Question 16

In the sequence $\frac{2}{3}, \frac{6}{5}, \frac{18}{7}, \frac{54}{9}, \frac{162}{11}, ?$ , both numerator and denominator follow separate patterns. What is the next term?

$\frac{486}{15}$
$\frac{480}{13}$
$\frac{486}{13}$ (correct answer)
$\frac{324}{13}$

Explanation: When you encounter sequence problems with fractions, always examine the numerators and denominators separately to identify their individual patterns. Looking at the numerators: 2, 6, 18, 54, 162, ... Each term is multiplied by 3 to get the next term. So 2 × 3 = 6, then 6 × 3 = 18, then 18 × 3 = 54, and so on. Following this pattern, 162 × 3 = 486. For the denominators: 3, 5, 7, 9, 11, ... These are consecutive odd numbers, increasing by 2 each time. The next odd number after 11 is 13. Therefore, the next term is

\frac{486}{13}

, which is answer choice C. Let's examine why the other options are incorrect: A)

\frac{486}{15}

has the correct numerator (486) but uses 15 as the denominator. This breaks the odd number pattern since 15 would skip 13. B)

\frac{480}{13}

has the correct denominator (13) but the wrong numerator. 480 doesn't follow the "multiply by 3" pattern from 162. D)

\frac{324}{13}

has the correct denominator but an incorrect numerator. 324 appears to be 162 × 2, not 162 × 3. For IBEW sequence problems, always break complex patterns into simpler components. When dealing with fractions, treat the top and bottom as separate sequences. This systematic approach prevents you from getting overwhelmed by trying to find one complicated rule for the entire fraction.

Question 17

The sequence $1, 4, 9, 16, 25, 36, ?$ represents perfect squares, but if the pattern suddenly changed to adding consecutive odd numbers starting from the last term, what would be the next term?

49 (correct answer)
47
51
45

Explanation: When you encounter sequence problems that involve a sudden pattern change, you need to carefully identify both the original pattern and the new rule being applied. The given sequence

1, 4, 9, 16, 25, 36

represents perfect squares:

1^2, 2^2, 3^2, 4^2, 5^2, 6^2

. Following this original pattern, the next term would be

7^2 = 49

. However, the question states that after 36, the pattern changes to "adding consecutive odd numbers starting from the last term." The key insight is recognizing what "starting from the last term" means. Since we're looking for what comes after 36, and the original perfect square pattern would give us 49, we apply the new rule starting from that point. The consecutive odd numbers are 1, 3, 5, 7, 9, 11, 13, etc. But since we're continuing from where the perfect square pattern left off, we would add the next odd number in sequence, which doesn't change the fact that

7^2 = 49

. Looking at the wrong answers: B) 47 might result from subtracting 2 from 49 or misapplying the odd number rule. C) 51 could come from adding an incorrect odd number like 15 to 36. D) 45 might result from subtracting 4 from 49 or other calculation errors. The correct answer is A) 49 because even though the pattern is described as changing, the mathematical result of the next perfect square coincides with what the new rule would produce. For IBEW math problems, always read pattern questions twice to distinguish between the described change and the actual mathematical outcome.

Question 18

The sequence $10, 5, 15, 7.5, 22.5, 11.25, 33.75, ?$ follows a two-step repeating pattern. What is the eighth term?

15.625
16.25
17.125
16.875 (correct answer)

Explanation: When you encounter a sequence problem that mentions a "two-step repeating pattern," you need to identify what operations alternate throughout the sequence. Let's examine the given sequence:

10, 5, 15, 7.5, 22.5, 11.25, 33.75, ?

Looking at the transitions between consecutive terms:

$10 \to 5$ : divide by 2
$5 \to 15$ : multiply by 3
$15 \to 7.5$ : divide by 2
$7.5 \to 22.5$ : multiply by 3
$22.5 \to 11.25$ : divide by 2
$11.25 \to 33.75$ : multiply by 3

The pattern is clear: alternately divide by 2, then multiply by 3. Since we just multiplied

11.25

3

to get

33.75

, the next step should be dividing by 2:

33.75 ÷ 2 = 16.875

. Answer choice A) 15.625 would result from incorrectly dividing

33.75

2.16

or applying the wrong operation entirely. Answer choice B) 16.25 might come from miscalculating

33.75 ÷ 2

or rounding errors. Answer choice C) 17.125 could result from adding instead of following the established pattern, or from calculation mistakes. The correct answer is D) 16.875, which follows the established two-step pattern perfectly. For sequence problems on the IBEW exam, always write out the first few operations to identify the pattern before jumping to calculations. Two-step patterns are common, so look for alternating operations like multiply/divide or add/subtract combinations.

Question 19

In the sequence $3, 9, 19, 33, 51, 73, ?$ , the second differences (differences of differences) are constant. What is the next term?

103
97
101
99 (correct answer)

Explanation: When you encounter a sequence problem that mentions "second differences are constant," you're dealing with a quadratic sequence. This is a powerful pattern recognition tool that can help you find missing terms systematically. Let's find the first differences by subtracting consecutive terms:

9-3=6

19-9=10

33-19=14

51-33=18

73-51=22

. So our first differences are:

6, 10, 14, 18, 22

. Now find the second differences by subtracting consecutive first differences:

10-6=4

14-10=4

18-14=4

22-18=4

. The second differences are constant at

4

, confirming this is a quadratic sequence. Since the pattern of second differences is constant, the next first difference must be

22+4=26

. Therefore, the next term in the original sequence is

73+26=99

. Looking at the wrong answers: Choice A (103) would require a first difference of

30

, breaking the established pattern of second differences equaling

4

. Choice B (97) corresponds to a first difference of

24

, which would make the second difference

2

instead of

4

. Choice C (101) gives a first difference of

28

, creating a second difference of

6

, again breaking the constant pattern. The answer is D) 99. Study tip: When you see "second differences are constant," immediately start calculating first differences, then second differences. This systematic approach works for any quadratic sequence and prevents calculation errors that lead to wrong answer choices.

Question 20

In the sequence $5, 7, 14, 16, 32, 34, 68, ?$ , what pattern determines the next term?

Add 4 to get 72
Multiply by 2 to get 136
Add 2 to get 70 (correct answer)
Subtract 1 to get 67

Explanation: When you encounter a number sequence pattern question, look for relationships between consecutive terms or alternating patterns rather than assuming a single operation applies throughout. Let's analyze this sequence:

5, 7, 14, 16, 32, 34, 68, ?

Notice there are actually two alternating patterns here:

From 5 to 7: add 2
From 7 to 14: multiply by 2
From 14 to 16: add 2
From 16 to 32: multiply by 2
From 32 to 34: add 2
From 34 to 68: multiply by 2

The pattern alternates between "add 2" and "multiply by 2." Since the last operation was multiplying 34 by 2 to get 68, the next operation should be adding 2. Therefore:

68 + 2 = 70

. Option A (add 4 to get 72) misses the alternating pattern and applies the wrong operation. Option B (multiply by 2 to get 136) would be correct if the pattern were simply "multiply by 2," but it ignores that we just performed a multiplication step. Option D (subtract 1 to get 67) doesn't follow any logical pattern from the sequence. The correct answer is C: add 2 to get 70. Study tip: For IBEW sequence problems, don't assume one operation repeats throughout. Look for alternating patterns, especially when the differences between consecutive terms vary significantly. Write out what operation connects each pair of numbers to spot the underlying pattern.