Number Series — Missing & Wrong Term — IBPS Clerk / SBI Clerk

Number series questions come in two closely related forms. A missing-term series gives most of a sequence and asks for the next (or a specific missing) term once the underlying rule is identified; a wrong-term series gives a COMPLETE sequence and asks which single term breaks an otherwise-consistent rule. Both demand the identical first step — find the rule — before either extending the sequence or checking every term against it.

1. Constant-difference and constant-ratio series

The two most basic series types are arithmetic (a constant amount added each step) and geometric (a constant ratio multiplied each step) — checking the difference between consecutive terms first, then the ratio if the difference isn't constant, identifies which type a series is. These resolve fastest since the rule, once spotted, requires no further searching.

2. Combined operation series

A combined-operation series applies a fixed formula each step, such as "double and add 1," rather than a single addition or multiplication. $4,9,19,39,79,\dots$ follows $\text{next}=2\times \text{previous}+1$ throughout: $2(4)+1=9$, $2(9)+1=19$, $2(19)+1=39$, and so on.

3. Alternating-operation series

An alternating series applies TWO different operations in a repeating cycle, rather than one fixed operation every step — recognising the cycle length (usually 2 or 3 steps) is the key to extending it correctly. $5,7,14,16,32,34,\dots$ alternates $+2$ then $\times 2$: $5+2=7$, $7\times 2=14$, $14+2=16$, $16\times 2=32$, and the cycle continues.

4. Formula-based series (squares, cubes, and their variants)

A formula-based series follows $f(n)$ for $n=1,2,3,\dots$, where $f(n)$ is a specific formula like $n^2+2n$ or $n^3+1$. Recognising a series as formula-based, rather than a step-by-step operation, usually requires noticing that consecutive DIFFERENCES themselves follow a recognisable pattern, like consecutive odd numbers or squares.

The series $3,8,15,24,35,48,63$ follows $n^2+2n$; its consecutive differences are $5,7,9,11,13,15$ — the odd numbers — which is the clue that reveals the underlying quadratic formula.

5. Second-order (difference-of-differences) series

When a series' own differences are not constant but form a RECOGNISABLE pattern themselves (their own arithmetic or geometric sequence), the series is second-order — extend the pattern of differences first, then add that next difference to the series' last term. $2,3,7,16,32,\dots$ has differences $1,4,9,16$ (perfect squares); the next difference is $25$, giving the next series term as $32+25=57$.

6. Wrong-term series: checking every term against the rule

A wrong-term question gives a complete sequence and requires testing EVERY term against a hypothesised rule — the moment one term fails to fit while the rest are consistent, that term is the wrong one, and its correct value can be derived by extending the true rule. Given $3,8,15,24,36,48,63$, checking against $n^2+2n$ ($3,8,15,24,35,48,63$) shows every term matches except the fifth, which should be 35, not 36 — making 36 the wrong term.

Worked Examples

Example 1. Find the next term: $4,9,19,39,79,\dots$

Each term follows "double and add 1": $2(79)+1=159$.

Answer: 159.

Example 2. Find the next term: $5,7,14,16,32,34,\dots$

The series alternates $+2$ then $\times 2$: after $34$, the next operation is $\times 2$: $34\times 2=68$.

Answer: 68.

Example 3. Find the next term: $2,9,28,65,126,\dots$

Each term follows $n^3+1$ for $n=1,2,3,4,5,\dots$: $1^3+1=2$, $2^3+1=9$, $3^3+1=28$, $4^3+1=65$, $5^3+1=126$. The next term uses $n=6$: $6^3+1=217$.

Answer: 217.

Example 4. Find the next term: $2,3,7,16,32,\dots$

The differences are $1,4,9,16$ — perfect squares. The next difference is $25$: $32+25=57$.

Answer: 57.

Example 5. Identify the wrong term: $3,8,15,24,36,48,63$.

Testing against $n^2+2n$: the correct sequence is $3,8,15,24,35,48,63$. The given sequence has $36$ in place of $35$.

Answer: 36 is the wrong term (should be 35).

Example 6. Identify the wrong term: $4,10,28,83,244$.

Testing the pattern "triple and subtract 2": $4\times 3-2=10$, $10\times 3-2=28$, $28\times 3-2=82$, $82\times 3-2=244$. The given sequence has $83$ in place of $82$.

Answer: 83 is the wrong term (should be 82).

Example 7. Find the next term: $5,8,13,21,34,\dots$

Each term is the sum of the two preceding terms (a Fibonacci-type series): $21+34=55$.

Answer: 55.

Summary

Missing-term and wrong-term questions both start with the identical step: identify the underlying rule. A missing-term question then extends the sequence using that rule; a wrong-term question checks every term against it to find the one that breaks the pattern.

Check constant difference (arithmetic) and constant ratio (geometric) first, since they resolve fastest. If neither fits, look for a fixed combined operation, an alternating cycle of two operations, or a formula like $n^2+2n$ or $n^3+1$ — a formula-based series is often revealed by its own differences following a recognisable pattern (consecutive odd numbers, squares, and so on).

A second-order series has differences that are not themselves constant but form their own recognisable sequence — extend that inner pattern first, then add the result to the series' last term.

For wrong-term questions, test the hypothesised rule against every term systematically; the single term that breaks an otherwise-consistent pattern is the answer, and the true rule reveals its correct value.