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TNPSC number series practice questions with patterns

By the PrepMatic team · Updated 9 Oct 2026 · 3 min read

Number series is listed under reasoning in the Group 4 syllabus, which has about 10 questions in Part C next to the aptitude block. Series questions look intimidating until you notice that there are only about eight patterns, and they are tested in a fixed order. The five questions below use five of them. See TNPSC aptitude and mental ability for the bigger picture.

What this topic covers

• Finding the next term of a series.
• Finding the missing term inside a series.
• Finding the wrong term, where one number breaks the pattern.
• Two interleaved series, where odd and even positions follow separate rules.

Check the patterns in this order. The first that fits is usually the answer.

Sample questions

Question 1

Find the next number in the series: 2, 6, 12, 20, 30, ?

• A. 40
• B. 42
• C. 44
• D. 36

Question 2

Find the next number in the series: 3, 5, 9, 17, 33, ?

• A. 49
• B. 57
• C. 65
• D. 66

Question 3

Find the next number in the series: 100, 95, 85, 70, 50, ?

• A. 25
• B. 20
• C. 30
• D. 15

Question 4

Find the next number in the series: 2, 3, 5, 7, 11, 13, ?

• A. 15
• B. 16
• C. 19
• D. 17

Question 5

Find the next number in the series: 1, 8, 27, 64, ?

• A. 125
• B. 100
• C. 216
• D. 81

Answers and explanations

1. B. The differences are 4, 6, 8, 10, so the next difference is 12 and the next term is 30 + 12 = 42. Another view: the terms are 1×2, 2×3, 3×4, 4×5, 5×6, so the next is 6×7 = 42.
2. C. Each difference doubles: 2, 4, 8, 16, so the next is 32 and the term is 33 + 32 = 65. Equivalently, each term is twice the previous one, minus 1.
3. A. The differences are −5, −10, −15, −20, so the next is −25 and the term is 50 − 25 = 25.
4. D. These are consecutive prime numbers, and the next prime after 13 is 17. The number 15 is divisible by 3 and 5, and 16 by 2, so they are not prime.
5. A. The terms are 1³, 2³, 3³, 4³, so the next is 5³ = 125.

How to prepare number series

Learn the eight patterns in the table until you can name them. Then practise with a stopwatch: give yourself 40 seconds per series. If none of the common patterns fits in 40 seconds, leave it and move on. A wrong answer in TNPSC costs nothing but a blank costs 0.5 mark, so use the last minutes of the paper to guess the series you skipped. The details are in the TNPSC marking scheme.

Write the differences between consecutive terms as the very first step, and then the differences of the differences. This one habit solves the first three questions above in under half a minute.

Keep a list of numbers worth knowing by heart: squares to 25, cubes to 10, primes below 50, and the triangular numbers 1, 3, 6, 10, 15, 21, 28. Series built from these are the commonest, and recognising them is faster than computing.

Related reasoning practice: TNPSC alpha-numeric reasoning practice uses the same pattern-finding skill on letters, and TNPSC simplification practice builds the arithmetic speed behind it.

Take the full topic test on PrepMatic

Reasoning gets quicker with timed practice. A PrepMatic topic test (about 15 questions, 30 minutes) helps you check how many series you can solve at exam speed. The free Basic plan includes 5 topic tests, and the free assessment shows whether reasoning and aptitude together are among your weakest subjects.

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