Number series sits in the quantitative section of IBPS, SBI and RBI papers, usually as a set of five questions, and it is one of the few topics where speed comes almost entirely from pattern recognition rather than calculation. Aspirants who work a fixed checklist consistently beat those who look for the answer by inspection.
Every question below was generated by the same engine that mints the Deduce daily puzzle, and machine-proven to have exactly one correct answer before it reached this page. The walkthrough is the engine's own, step for step.
What number replaces the question mark?
36, 49, 64, 81, 100, ?
What number replaces the question mark?
5, ?, 8, 11, 15
What number replaces the question mark?
3, 10, ?, 52, 108, 220, 444
Subtract each term from the next. If the differences are constant the series is arithmetic; if they form a recognisable run such as 2, 4, 6, 8 or 1, 4, 9, 16, you already have the rule.
When the first differences are not obvious, difference them again. A constant second difference means a quadratic pattern, which covers a large share of exam series.
Divide each term by the previous one. A constant ratio is geometric; a ratio that moves in a clean run — ×2, ×3, ×4 — is just as common and is missed by anyone who only ever subtracts.
Compare each term with the nearby square or cube. Patterns like n² + 1 or n³ − 2 are frequent, and they look random until you line the sequence up against 1, 4, 9, 16, 25.
If the sequence alternates between rising and falling, or nothing fits, split it into odd and even positions and test each half separately. Alternating series are a standard trap.
A rule that explains four of five terms is the wrong rule. Run it across the whole sequence, including the ones you were confident about, before committing.
| Signature | Likely rule |
|---|---|
| Constant first difference | Arithmetic — add a fixed number |
| First differences form a run (2, 4, 6, 8) | Add an increasing step |
| Constant second difference | Quadratic pattern |
| Constant ratio | Geometric — multiply by a fixed number |
| Ratio itself increases (×2, ×3, ×4) | Multiply by an increasing factor |
| Terms sit just off 1, 4, 9, 16, 25 | Squares or cubes with a small offset |
| Sequence alternates up and down | Two interleaved series — split odd and even positions |
The most common error is finding a pattern that works for the first few terms and stopping. Every exam series has exactly one rule that fits all of it; test yours across every term.
Candidates who default to differences miss geometric and multiplicative series entirely. If two rounds of differences produce nothing, switch to ratios rather than differencing a third time.
Series questions are all-or-nothing and independent of each other. If the pattern has not appeared in about ninety seconds, move on and return with the time you saved on the rest of the set.
One puzzle a day, timed on the server, with a national and state leaderboard and a streak that survives as long as you do. Practising a topic once is worth little; the aspirants who move are the ones who show up daily. See what Deduce does or read the rules first.
Start your streak free →Work a fixed checklist instead of staring at the numbers: first differences, then second differences, then ratios, then nearby squares and cubes with a small offset, then a split into two interleaved series. Most exam series resolve in the first two steps, and the checklist stops you from missing multiplicative patterns.
Subtract consecutive terms and divide consecutive terms. A constant difference means arithmetic; a constant ratio means geometric. If neither is constant but one of them forms a clean run — differences going 2, 4, 6, 8 or ratios going ×2, ×3, ×4 — that run is itself the rule.
It is a variant where every term follows one rule except a single term that breaks it, and you must identify the odd one out rather than continue the sequence. Find the rule from the terms that agree, then check each remaining term against it; the one that fails is the answer.
IBPS and SBI prelims typically carry a set of five in the quantitative section, and mains papers often include a harder wrong-number set. Because the questions are independent, the section rewards attempting the ones you see quickly and leaving the rest rather than working through them in order.
Deduce is not affiliated with IBPS, SBI, SSC or RBI.