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Number series questions with answers

These number series questions ask for a missing or wrong term, and every one is solvable from the differences alone — no pattern here needs an intuition you either have or do not. The walkthrough under each question prints the difference row the solver used, which is the working most people skip and then cannot reconstruct when the answer comes out wrong.

Download the PDF — 15 questions with answers

Free, ungated, no email. This is the number series questions with answers PDF — the same 15 questions as below, with every worked solution at the back, ready to print.

How to use this set

The 15 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 15 sit in the hard band. Every question is a number series (find the missing term).

Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: Number series: read the differences first.

15 number series questions with answers

Every question below was generated by the same engine that mints the DeducePuzzles daily puzzle round, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own.

Question 1

What number replaces the question mark?

3, 6, ?, 24, 48

  1. 11
  2. 12
  3. 14
  4. 10
  5. 13
Show the worked solution
  1. The rule is: geometric (constant ratio).
  2. Consecutive ratios are constant: 6/3=2, 12/6=2, 24/12=2, 48/24=2.
  3. Applying the rule, the value at the "?" is 12.

Question 2

What number replaces the question mark?

6, 18, 54, 162, 486, ?

  1. 1456
  2. 1460
  3. 1459
  4. 1457
  5. 1458
Show the worked solution
  1. The rule is: geometric (constant ratio).
  2. Consecutive ratios are constant: 18/6=3, 54/18=3, 162/54=3, 486/162=3, 1458/486=3.
  3. Applying the rule, the value at the "?" is 1458.

Question 3

Find the wrong number in the series.

4, 12, 42, 132, 402, 1212

  1. 4
  2. 12
  3. 42
  4. 132
  5. 402
Show the worked solution
  1. The rule is: ×k then +c (multiply then add).
  2. Each term comes from the previous term by the same multiply-then-add operation.
  3. Every term fits that rule except the 1st term: the rule gives 2 there, but the series shows 4.
  4. So the wrong number is 4; it should be 2.

Question 4

Find the wrong number in the series.

8, 13, 20, 30, 40, 53

  1. 8
  2. 20
  3. 30
  4. 40
  5. 53
Show the worked solution
  1. The rule is: increasing differences (differences in arithmetic progression).
  2. Consecutive differences are 5, 7, 9, 11, 13; those differences themselves follow an arithmetic pattern.
  3. Every term fits that rule except the 4th term: the rule gives 29 there, but the series shows 30.
  4. So the wrong number is 30; it should be 29.

Question 5

Find the wrong number in the series.

7, 9, 10, 16, 21, 27

  1. 7
  2. 10
  3. 16
  4. 21
  5. 27
Show the worked solution
  1. The rule is: increasing differences (differences in arithmetic progression).
  2. Consecutive differences are 2, 3, 4, 5, 6; those differences themselves follow an arithmetic pattern.
  3. Every term fits that rule except the 3rd term: the rule gives 12 there, but the series shows 10.
  4. So the wrong number is 10; it should be 12.

Question 6

What number replaces the question mark?

5, 7, ?, 13, 17, 19

  1. 13
  2. 12
  3. 10
  4. 11
  5. 9
Show the worked solution
  1. The rule is: consecutive prime numbers.
  2. The terms are consecutive prime numbers in order.
  3. Applying the rule, the value at the "?" is 11.

Question 7

What number replaces the question mark?

3, 12, 21, ?, 39, 48

  1. 32
  2. 31
  3. 30
  4. 29
  5. 28
Show the worked solution
  1. The rule is: arithmetic (constant difference).
  2. Consecutive differences are constant: 9, 9, 9, 9, 9.
  3. Applying the rule, the value at the "?" is 30.

Question 8

What number replaces the question mark?

4, 9, 16, 25, 36, ?

  1. 51
  2. 50
  3. 49
  4. 48
  5. 47
Show the worked solution
  1. The rule is: consecutive perfect squares.
  2. The terms are consecutive perfect squares.
  3. Applying the rule, the value at the "?" is 49.

Question 9

What number replaces the question mark?

33, 46, 61, ?, 97, 118

  1. 78
  2. 76
  3. 79
  4. 77
  5. 80
Show the worked solution
  1. The rule is: perfect squares (with constant offset).
  2. Compare the terms with consecutive perfect squares; the same constant offset is applied throughout.
  3. Applying the rule, the value at the "?" is 78.

Question 10

Find the wrong number in the series.

4, 18, 60, 186, 566, 1698, 5100

  1. 18
  2. 60
  3. 186
  4. 566
  5. 5100
Show the worked solution
  1. The rule is: ×k then +c (multiply then add).
  2. Each term comes from the previous term by the same multiply-then-add operation.
  3. Every term fits that rule except the 5th term: the rule gives 564 there, but the series shows 566.
  4. So the wrong number is 566; it should be 564.

Question 11

What number replaces the question mark?

4, 8, 13, 19, 26, 34, ?

  1. 43
  2. 45
  3. 44
  4. 41
  5. 42
Show the worked solution
  1. The rule is: increasing differences (differences in arithmetic progression).
  2. Consecutive differences are 4, 5, 6, 7, 8, 9; those differences themselves follow an arithmetic pattern.
  3. Applying the rule, the value at the "?" is 43.

Question 12

Find the wrong number in the series.

3, 4, 7, 12, 18, 29

  1. 3
  2. 4
  3. 12
  4. 18
  5. 29
Show the worked solution
  1. The rule is: Fibonacci-like (each term is the sum of the previous two).
  2. From the third term onward, each term equals the sum of the previous two terms.
  3. Every term fits that rule except the 4th term: the rule gives 11 there, but the series shows 12.
  4. So the wrong number is 12; it should be 11.

Question 13

What number replaces the question mark?

6, 24, 96, 384, 1536, ?

  1. 6144
  2. 6142
  3. 6143
  4. 6146
  5. 6145
Show the worked solution
  1. The rule is: geometric (constant ratio).
  2. Consecutive ratios are constant: 24/6=4, 96/24=4, 384/96=4, 1536/384=4, 6144/1536=4.
  3. Applying the rule, the value at the "?" is 6144.

Question 14

What number replaces the question mark?

16, ?, 36, 49, 64, 81

  1. 27
  2. 25
  3. 26
  4. 23
  5. 24
Show the worked solution
  1. The rule is: consecutive perfect squares.
  2. The terms are consecutive perfect squares.
  3. Applying the rule, the value at the "?" is 25.

Question 15

Find the wrong number in the series.

13, 20, 29, 38, 53, 68

  1. 20
  2. 29
  3. 38
  4. 53
  5. 68
Show the worked solution
  1. The rule is: perfect squares (with constant offset).
  2. Compare the terms with consecutive perfect squares; the same constant offset is applied throughout.
  3. Every term fits that rule except the 4th term: the rule gives 40 there, but the series shows 38.
  4. So the wrong number is 38; it should be 40.
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Where these questions come from

Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves DeducePuzzles's daily puzzle round, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded.

If you want the method rather than more questions, Number series: read the differences first covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is how do I solve these, this one is give me number series questions with the answers.

FAQ

What should I check first in a number series?

The first differences. Write them under the series. Constant means arithmetic; a pattern in the differences means take second differences; a roughly constant ratio means geometric. Only when all three fail should you look for squares, cubes or alternating sub-series.

How do I spot an alternating series?

The differences swing between two very different magnitudes. Split the series into odd and even positions and treat each as its own series — an alternating pattern is two simple series interleaved, and each half is almost always trivial once separated.

Are wrong-term questions solved differently from missing-term ones?

Slightly. Establish the rule from the terms that agree, then find the single term that breaks it. Beginners recompute the whole series from the first term, which propagates the error and makes every later term look wrong. Trust the majority pattern and hunt the outlier.

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