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Number Series Questions with Solutions

Number Series questions test pattern recognition — the pattern is usually one of a small set of standard types, and finding which one applies is the whole game. Here’s the approach, four fully worked examples covering the patterns that come up most, and a few to try yourself.

The approach, quickly

  • First check the simple difference between consecutive terms. If that’s constant, you have a plain arithmetic series.
  • If the plain difference isn’t constant, check whether the DIFFERENCES themselves follow a pattern (e.g., 3, 5, 7, 9, …) — this catches series built from squares, cubes or similar formulas.
  • If differences don’t help, check the ratio between consecutive terms (geometric series), or try splitting the series into its odd-position and even-position terms separately — many series are really two simpler series interleaved.
  • Always check your guessed pattern against every given term, not just the first two or three — a pattern that fits the start can still break later in the sequence.

Worked examples

1. Find the next number in the series: 2, 5, 10, 17, 26, ?

Solution

  1. Differences between consecutive terms: 5−2=3, 10−5=5, 17−10=7, 26−17=9.
  2. The differences themselves are 3, 5, 7, 9 — increasing by 2 each time, so the next difference is 11.
  3. Next term = 26 + 11 = 37. (This series is actually n² + 1 for n = 1, 2, 3, …)

Answer: 37

2. Find the next number in the series: 3, 6, 12, 24, 48, ?

Solution

  1. Each term is double the previous one: 6/3=2, 12/6=2, 24/12=2, 48/24=2.
  2. Next term = 48 × 2 = 96.

Answer: 96

3. Find the missing number in the series: 1, 4, 2, 8, 3, 12, 4, ?

Solution

  1. This looks irregular as one sequence, so split it into odd-position and even-position terms.
  2. Odd positions (1st, 3rd, 5th, 7th): 1, 2, 3, 4 — increasing by 1 each time.
  3. Even positions (2nd, 4th, 6th, 8th): 4, 8, 12, ? — increasing by 4 each time, so the next (8th) term is 16.

Answer: 16

4. Find the next number in the series: 5, 8, 4, 7, 3, 6, 2, ?

Solution

  1. Check the pattern of operations rather than a single constant difference: 5→8 is +3, 8→4 is −4, 4→7 is +3, 7→3 is −4, 3→6 is +3, 6→2 is −4.
  2. The operations alternate +3, −4, +3, −4, … and the last one shown was −4 (6→2), so the next one is +3.
  3. Next term = 2 + 3 = 5.

Answer: 5

Try these yourself

Find the pattern the same way, then check against the answer.

1. Find the next number in the series: 3, 7, 13, 21, 31, ?

Answer: 43 (differences 4, 6, 8, 10, 12)

2. Find the next number in the series: 2, 6, 18, 54, ?

Answer: 162 (each term × 3)

3. Find the missing number in the series: 2, 3, 4, 6, 6, 9, 8, ?

Answer: 12 (odd positions +2 each: 2,4,6,8; even positions +3 each: 3,6,9,12)

Where this comes up

Number Series is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.

Practice more Number Series questions

This page covers the approach and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Number Series (and every other Reasoning/Quant/English topic) with instant scoring and explanations — free, no account required.

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