Number Series Questions and Answers

Q: The run below is governed by one rule from beginning to end. Find the rule and name the term that completes the run.75, 62, 49, 36, ?

Correct answer: 23Every gap is the same: the differences run -13, -13, -13, so the common difference is -13. Applying it once more to the final term, 36 - 13 gives 23. As a check, subtracting -13 from the answer returns 36, the term before it, and repeating that recovers the whole series. Reading a series backwards sometimes turns an awkward rule into a familiar one.

Q: A single relationship connects every term shown here. Find the rule and name the term that completes the run.11, 25, 39, 53, ?

Correct answer: 67Every gap is the same: the differences run 14, 14, 14, so the common difference is 14. Applying it once more to the final term, 53 + 14 gives 67. As a check, subtracting 14 from the answer returns 53, the term before it, and repeating that recovers the whole series. The last term is the one most often misread, and re-checking it costs nothing.

Q: The terms below were produced by applying the same operation repeatedly. Find the rule and name the term that completes the run.3, 28, 53, 78, ?

Correct answer: 103Every gap is the same: the differences run 25, 25, 25, so the common difference is 25. Applying it once more to the final term, 78 + 25 gives 103. As a check, subtracting 25 from the answer returns 78, the term before it, and repeating that recovers the whole series. Odd and even terms behaving differently is the first sign of an interleaved rather than a single series.

Q: One number has been withheld from the end of this sequence. Find the rule and name the term that completes the run.18, 40, 62, 84, ?

Correct answer: 106Every gap is the same: the differences run 22, 22, 22, so the common difference is 22. Applying it once more to the final term, 84 + 22 gives 106. As a check, subtracting 22 from the answer returns 84, the term before it, and repeating that recovers the whole series. A large jump between two terms usually means multiplication rather than addition.

Q: The sequence below breaks off before its final term. Find the rule and name the term that completes the run.200, 183, 166, 149, ?

Correct answer: 132Every gap is the same: the differences run -17, -17, -17, so the common difference is -17. Applying it once more to the final term, 149 - 17 gives 132. As a check, subtracting -17 from the answer returns 149, the term before it, and repeating that recovers the whole series. Where every term is even, the rule usually involves a factor of two somewhere.

Q: Every term here follows from the one before it, or from its own position. Find the rule and name the term that completes the run.27, 40, 53, 66, ?

Correct answer: 79Every gap is the same: the differences run 13, 13, 13, so the common difference is 13. Applying it once more to the final term, 66 + 13 gives 79. As a check, subtracting 13 from the answer returns 66, the term before it, and repeating that recovers the whole series. Units digits often follow a short cycle, which can confirm an answer without the full arithmetic.

Q: The numbers below are not random; a rule accounts for all of them. Find the rule and name the term that completes the run.45, 36, 27, 18, 9, ?

Correct answer: 0Every gap is the same: the differences run -9, -9, -9, -9, so the common difference is -9. Applying it once more to the final term, 9 - 9 gives 0. As a check, subtracting -9 from the answer returns 9, the term before it, and repeating that recovers the whole series. A quick estimate of the expected size of the answer eliminates at least one option in most questions of this kind.

Q: This run continues in a way the terms shown are enough to determine. Find the rule and name the term that completes the run.8, 26, 44, 62, ?

Correct answer: 80Every gap is the same: the differences run 18, 18, 18, so the common difference is 18. Applying it once more to the final term, 62 + 18 gives 80. As a check, subtracting 18 from the answer returns 62, the term before it, and repeating that recovers the whole series. The options are constructed so that each corresponds to a specific misreading, which makes guessing unprofitable.

Q: The list below is incomplete by exactly one term. Find the rule and name the term that completes the run.2, 14, 98, 686, ?

Correct answer: 4802The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 14 over 2 is 7, and 98 over 14 is 7, so the ratio is 7. Multiplying the last term, 686 times 7 is 4802. As a check, dividing the answer by 7 returns 686, which is the last term shown. Working the rule backwards from the answer to the first term is the most reliable check available.

Q: A rule that fits every term shown will also give the missing one. Find the rule and name the term that completes the run.9, 27, 81, 243, ?

Correct answer: 729The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 27 over 9 is 3, and 81 over 27 is 3, so the ratio is 3. Multiplying the last term, 243 times 3 is 729. As a check, dividing the answer by 3 returns 243, which is the last term shown. If two different rules both fit, the simpler is intended; series questions do not reward ingenuity beyond the obvious.

Important Instructions

141.

The run below is governed by one rule from beginning to end. Find the rule and name the term that completes the run.
75, 62, 49, 36, ?

A.23
B.10
C.-3
D.24

Answer: C

Correct answer: 23

Every gap is the same: the differences run -13, -13, -13, so the common difference is -13. Applying it once more to the final term, 36 - 13 gives 23. As a check, subtracting -13 from the answer returns 36, the term before it, and repeating that recovers the whole series. Reading a series backwards sometimes turns an awkward rule into a familiar one.

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142.

A single relationship connects every term shown here. Find the rule and name the term that completes the run.
11, 25, 39, 53, ?

A.81
B.67
C.95
D.68

Answer: D

Correct answer: 67

Every gap is the same: the differences run 14, 14, 14, so the common difference is 14. Applying it once more to the final term, 53 + 14 gives 67. As a check, subtracting 14 from the answer returns 53, the term before it, and repeating that recovers the whole series. The last term is the one most often misread, and re-checking it costs nothing.

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143.

The terms below were produced by applying the same operation repeatedly. Find the rule and name the term that completes the run.
3, 28, 53, 78, ?

A.128
B.153
C.103
D.104

Answer: A

Correct answer: 103

Every gap is the same: the differences run 25, 25, 25, so the common difference is 25. Applying it once more to the final term, 78 + 25 gives 103. As a check, subtracting 25 from the answer returns 78, the term before it, and repeating that recovers the whole series. Odd and even terms behaving differently is the first sign of an interleaved rather than a single series.

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144.

One number has been withheld from the end of this sequence. Find the rule and name the term that completes the run.
18, 40, 62, 84, ?

A.128
B.150
C.107
D.106

Answer: B

Correct answer: 106

Every gap is the same: the differences run 22, 22, 22, so the common difference is 22. Applying it once more to the final term, 84 + 22 gives 106. As a check, subtracting 22 from the answer returns 84, the term before it, and repeating that recovers the whole series. A large jump between two terms usually means multiplication rather than addition.

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145.

The sequence below breaks off before its final term. Find the rule and name the term that completes the run.
200, 183, 166, 149, ?

A.132
B.115
C.98
D.133

Answer: C

Correct answer: 132

Every gap is the same: the differences run -17, -17, -17, so the common difference is -17. Applying it once more to the final term, 149 - 17 gives 132. As a check, subtracting -17 from the answer returns 149, the term before it, and repeating that recovers the whole series. Where every term is even, the rule usually involves a factor of two somewhere.

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146.

Every term here follows from the one before it, or from its own position. Find the rule and name the term that completes the run.
27, 40, 53, 66, ?

A.92
B.79
C.105
D.80

Answer: D

Correct answer: 79

Every gap is the same: the differences run 13, 13, 13, so the common difference is 13. Applying it once more to the final term, 66 + 13 gives 79. As a check, subtracting 13 from the answer returns 66, the term before it, and repeating that recovers the whole series. Units digits often follow a short cycle, which can confirm an answer without the full arithmetic.

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147.

The numbers below are not random; a rule accounts for all of them. Find the rule and name the term that completes the run.
45, 36, 27, 18, 9, ?

A.-9
B.-18
C.0
D.1

Answer: A

Correct answer: 0

Every gap is the same: the differences run -9, -9, -9, -9, so the common difference is -9. Applying it once more to the final term, 9 - 9 gives 0. As a check, subtracting -9 from the answer returns 9, the term before it, and repeating that recovers the whole series. A quick estimate of the expected size of the answer eliminates at least one option in most questions of this kind.

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148.

This run continues in a way the terms shown are enough to determine. Find the rule and name the term that completes the run.
8, 26, 44, 62, ?

A.98
B.116
C.81
D.80

Answer: B

Correct answer: 80

Every gap is the same: the differences run 18, 18, 18, so the common difference is 18. Applying it once more to the final term, 62 + 18 gives 80. As a check, subtracting 18 from the answer returns 62, the term before it, and repeating that recovers the whole series. The options are constructed so that each corresponds to a specific misreading, which makes guessing unprofitable.

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149.

The list below is incomplete by exactly one term. Find the rule and name the term that completes the run.
2, 14, 98, 686, ?

A.4802
B.4116
C.5488
D.33614

Answer: C

Correct answer: 4802

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 14 over 2 is 7, and 98 over 14 is 7, so the ratio is 7. Multiplying the last term, 686 times 7 is 4802. As a check, dividing the answer by 7 returns 686, which is the last term shown. Working the rule backwards from the answer to the first term is the most reliable check available.

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150.

A rule that fits every term shown will also give the missing one. Find the rule and name the term that completes the run.
9, 27, 81, 243, ?

A.486
B.729
C.972
D.2187

Answer: D

Correct answer: 729

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 27 over 9 is 3, and 81 over 27 is 3, so the ratio is 3. Multiplying the last term, 243 times 3 is 729. As a check, dividing the answer by 3 returns 243, which is the last term shown. If two different rules both fit, the simpler is intended; series questions do not reward ingenuity beyond the obvious.

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Number Series Questions and Answers

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