Number Sequence Test: Practice Questions and Answers

To solve a number sequence question, compare neighboring terms, look for a rule, and check that rule against every number shown. Start with differences and ratios. If neither is consistent, look for changing differences, alternating operations, or two interleaved sequences.

Try this: 6, 11, 18, 27, 38, ?. The gaps are 5, 7, 9, 11. Continuing that pattern gives a gap of 13, so the next term is 51. The useful step is recognizing the pattern in the gaps, not guessing from the last two numbers.

Below are eight original practice questions, worked answers, and a short retest. You can use them without an account. They are learning exercises, not a reproduction of any employer's test, and their results do not provide an IQ score or hiring benchmark.

A repeatable method for finding the next number

Use this order as a starting point. Some questions fit more than one description.

A constant difference defines an arithmetic sequence; a constant ratio defines a geometric sequence. OpenStax's introduction to sequences explains these definitions. The mixed patterns in this article are additional practice examples.

Before accepting a rule, test it from the beginning. “Multiply by two” fits the first step in 3, 6, 7, 14, 15 but fails at the next one. Repeating two operations explains every transition shown.

Practice set: eight number sequence questions

For each row, write the next number and a sentence describing your rule. Work untimed on your first attempt. If you time a later attempt, record your own elapsed time; there is no official timer or pass score for this set.

Show all eight worked answers

▸1. Constant addition: 45

Every gap is 7: 24 − 17 = 7, 31 − 24 = 7, and 38 − 31 = 7. Continue with 38 + 7 = 45.

▸2. Repeated halving: 12

Each term is half the previous term. 24 ÷ 2 = 12. Equivalently, the common ratio is 1/2; a geometric sequence can decrease.

▸3. Consecutive squares: 49

The terms are 2², 3², 4², 5², 6². The next is 7² = 49. You can also check the differences: 5, 7, 9, 11, followed by 13.

▸4. Increasing gaps: 48

Subtract neighboring terms to get 4, 6, 8, 10. These gaps increase by 2. The next gap is 12, giving 36 + 12 = 48. Adding 10 again would ignore the changing pattern.

▸5. Alternating ×2 and +3: 58

The transitions are 5 × 2 = 10, 10 + 3 = 13, 13 × 2 = 26, and 26 + 3 = 29. The next operation is ×2, so the answer is 29 × 2 = 58.

▸6. Two interleaved sequences: 11

Read positions 1, 3, and 5: 2, 5, 8. They increase by 3. Positions 2, 4, and 6 are 40, 35, 30, decreasing by 5. The missing seventh term belongs to the first sequence, so it is 11. If asked for the eighth term, it would be 25.

▸7. Add the previous two terms: 47

Starting with the third term, each term is the sum of the previous two: 4 + 7 = 11, 7 + 11 = 18, and 11 + 18 = 29. Continue with 18 + 29 = 47. Recognize the recurrence without assuming that every such sequence must begin with 1 and 1.

▸8. Multiply by three, then subtract one: 608

Use the same two-step operation each time: 3 × 3 − 1 = 8, 8 × 3 − 1 = 23, 23 × 3 − 1 = 68, and 68 × 3 − 1 = 203. The next term is 203 × 3 − 1 = 608. Both operations occur at every transition; they do not alternate between transitions.

Why a short sequence can have more than one answer

A finite list of numbers does not uniquely determine every future term unless you are also given the generating rule or other constraints. These exercises ask you to continue the simple patterns described in the answers. Another consistent rule can sometimes generate a different continuation.

In a multiple-choice assessment, check the proposed rule against the entire sequence and the available choices. In an open-ended exercise, state your rule. If two simple rules fit, acknowledge that ambiguity instead of pretending the next number is mathematically forced.

This is also why memorizing a list of answers is weak preparation. You need a way to explain why a rule fits, including the awkward middle terms.

Turn mistakes into a practice target

Separate pattern recognition from arithmetic. A wrong answer to question 6 might mean you did not notice the alternating positions. A wrong answer to question 8 might mean you found the rule but calculated 203 × 3 incorrectly. Those errors need different practice.

If your goal is a timed arithmetic assessment, the Zetamac improvement guide covers a separate baseline-and-drill routine. Zetamac-style speed practice helps rehearse calculations; it does not by itself teach sequence recognition.

Retest with four fresh examples

After reviewing your errors, try a new set rather than immediately repeating questions whose answers you remember. Use the same approach: next term plus a rule.

1. ▸19, 27, 35, 43, ?
2. ▸7, 14, 17, 34, 37, ?
3. ▸3, 50, 7, 44, 11, 38, ?
4. ▸5, 9, 15, 23, 33, ?

Show retest answers

1. ▸51: add 8 each time.
2. ▸74: alternate ×2 and +3; the next operation is ×2.
3. ▸15: odd positions are 3, 7, 11, 15; even positions are 50, 44, 38, falling by 6.
4. ▸45: gaps are 4, 6, 8, 10; add 12 next.

Record which types you can explain without help. Return on another day and create a fresh example using the same kind of rule. A better result on memorized questions does not establish better performance on unfamiliar sequences.

Is this the same as NumberLogic or a Zetamac test?

These are general number-sequence exercises. If your assessment invitation calls a section “NumberLogic,” use that invitation for its instructions, timing, and scoring. This page does not verify a particular employer's format or reproduce its question bank.

Zetamac is an arithmetic speed drill, where the operation is already given. Here you first have to infer a pattern. For candidates comparing arithmetic preparation formats, our Optiver 80-in-8 and Zetamac guide explains the limits of that comparison. For reasoning practice with probabilities, try the original exercises in our Jane Street trading interview guide.

If you recognized the patterns but the calculations slowed you down, finish a Basics run, review the weak skills, and then return to a fresh sequence. If recognizing the pattern was the difficulty, work through another sequence explanation before adding time pressure.