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Number Series Tricks for Bank Exams: Missing and Wrong Terms

Check the growth • Differences and second differences • ×n + n patterns • Powers • Alternating series • Wrong term

Banking 📅 Last updated: 2026-10-24

Number series questions in bank prelims give five to seven terms and ask for the missing or the wrong one. There are only a handful of rule families, and the fastest way to find the right one is to look at how the series grows before calculating anything.

What you seeTest first
Slow, steady riseDifferences, then second differences
Roughly doubling or tripling×n, ×n + k, or ×n − k
Fast, curved riseSquares, cubes, or powers ± k
Rise with a jump that keeps growing×1 + 1, ×2 + 2, ×3 + 3 …
Up and downTwo alternating series
Falling fastDivision by a changing number

Spend a couple of seconds on this classification. It usually rules out most families at once, so you test one or two rules instead of six.

Write the differences between consecutive terms under the series. If they form a simple pattern, you are done.

Worked example 1: differences that rise by 2

7, 11, 17, 25, 35, ? The differences are 4, 6, 8, 10, so the next is 12 and the missing term is 35 + 12 = 47.

If the first differences are not regular, take the differences again. A constant second difference is common.

Worked example 2: second differences

1, 3, 8, 16, 27, ? First differences: 2, 5, 8, 11. Their differences are all 3, so the next first difference is 14 and the answer is 27 + 14 = 41.

When terms roughly double, divide each term by the one before it. A ratio of a little over 2 points to "×2 plus something".

Worked example 3: ×2 + 1

3, 7, 15, 31, 63, ? Each term is 2 × previous + 1, so the next is 63 × 2 + 1 = 127.

A very common bank pattern uses a multiplier and an addition that both increase by one each step.

Worked example 4: ×1 + 1, ×2 + 2, ×3 + 3 …

5, 6, 14, 45, ? Here 5 × 1 + 1 = 6, 6 × 2 + 2 = 14 and 14 × 3 + 3 = 45, so the next is 45 × 4 + 4 = 184.

Check the rule on every given term before trusting it: starting from 5, the three steps give 6, 14 and 45, which matches the printed series.

Learn the squares to 30 and the cubes to 15. Then series built on them, often with ±1 or ±2, are easy to spot.

Worked example 5: squares plus one

2, 5, 10, 17, 26, ? These are 1² + 1, 2² + 1, 3² + 1, 4² + 1 and 5² + 1, so the next is 6² + 1 = 37.

If the terms go up and down, split the series into odd and even positions and treat each as its own series.

Worked example 6: two series interleaved

4, 9, 8, 15, 16, 21, ? Odd positions: 4, 8, 16 (doubling). Even positions: 9, 15, 21 (adding 6). The seventh term is on the doubling series: 16 × 2 = 32.

In a wrong-number question, every term is printed but one breaks the rule. Find the rule from a run of terms that agree, then recompute each term in turn.

Worked example 7: n(n + 1)

2, 6, 12, 20, 31, 42. The terms fit 1 × 2, 2 × 3, 3 × 4, 4 × 5 and 6 × 7, so the fifth term should be 5 × 6 = 30. The wrong number is 31.

The term after the wrong one is the best confirmation. Here 42 = 6 × 7 fits, so the rule holds and only 31 is out of place.

  • ✘ Fixing on the first rule that fits two terms without testing it on the rest.
  • ✘ Missing an alternating series because you only looked at consecutive differences.
  • ✘ In wrong-number questions, choosing the term after the error, which only looks wrong because it was computed from a correct value.
  • ✘ Not knowing squares and cubes well enough to recognise them instantly.

Number series sits alongside approximation and simplification, quantity comparison and data sufficiency in bank prelims. For the powers you need, see square and cube roots and the Quant cheat code.

Q1. Find the next term: 6, 13, 27, 55, ? easy

✅ Answer: (b) 111

💡 Explanation: Each term is double the previous plus 1: 6 × 2 + 1 = 13, 13 × 2 + 1 = 27, 27 × 2 + 1 = 55, so the next is 55 × 2 + 1 = 111.

Q2. Find the next term: 120, 60, 20, 5, ? easy

✅ Answer: (c) 1

💡 Explanation: The divisors grow by one each step: ÷2 gives 60, ÷3 gives 20, ÷4 gives 5, so the next step is ÷5, giving 1.

Q3. Find the next term: 1, 8, 27, 64, 125, ? easy

✅ Answer: (d) 216

💡 Explanation: The terms are the cubes 1³, 2³, 3³, 4³ and 5³. The next is 6³ = 216. 196 is 14², a square-series trap.

Q4. Find the wrong number: 3, 5, 9, 17, 34, 65 medium

✅ Answer: (a) 34

💡 Explanation: The rule is ×2 − 1: 3 → 5 → 9 → 17 → 33 → 65. The fifth term should be 17 × 2 − 1 = 33, so 34 is wrong; 65 = 33 × 2 − 1 confirms the rule.

Q5. Find the next term: 2, 3, 7, 16, 32, ? medium

✅ Answer: (c) 57

💡 Explanation: The differences are 1, 4, 9 and 16, the squares of 1 to 4. The next difference is 5² = 25, so the next term is 32 + 25 = 57.

Q6. Find the next term: 11, 13, 17, 19, 23, ? medium

✅ Answer: (c) 29

💡 Explanation: These are consecutive prime numbers. After 23, 25 = 5 × 5 and 27 = 3 × 9 are not prime, so the next prime is 29.

How do I decide which pattern to test first?

Look at how fast the series grows. Slow, steady growth suggests differences; growth that roughly doubles or triples suggests multiplication; a fast, curved rise suggests squares or cubes; and terms that go up and down suggest an alternating or mixed series.

How is a wrong-number series different from a missing-number series?

In a wrong-number series every term is printed but one breaks the rule. Find the rule from the terms that fit, usually the first three or four, then recompute each term. The one that does not match is the answer, and the term after it confirms the rule.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 14 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-24 against the sources listed above.

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