Number Series — IBPS PO Quantitative Aptitude

A number series question is a small pattern to diagnose, not to solve by algebra. IBPS gives you 3–5 per paper in two flavours — missing term (find the ?) and wrong term (which number breaks the pattern) — and the entire skill is recognising which family of pattern you're looking at, fast. The good news: there are only about six families, and a two-second glance at the gaps between terms tells you which one. Train the recognition and this becomes 15-second marks; skip the training and you stare.

1. What IBPS actually asks

• Missing term: 4, 6, 9, 13.5, ? — find the next/blank value.
• Wrong term: 3, 5, 12, 38, 154, 809 — identify the term that doesn't fit the rule.

Both reward the same diagnosis. In Prelims, series questions are among the fastest quant marks; in Mains they get one or two harder (double-pattern) members.

2. Diagnose by the gaps — the 15-second habit

Before trying anything clever, compute the differences between consecutive terms. The gap pattern reveals the family:

• Constant gap → arithmetic (add/subtract a fixed number).
• Gaps growing by a constant → the difference is itself an AP (second difference constant).
• Gaps that multiply → the ratio is the pattern (geometric), or a ×n rule.
• Gaps = 2, 4, 6, 8… or 1, 4, 9, 16… → differences are multiples or squares/cubes.

If the gaps don't resolve it, check the ratio of consecutive terms next. Gap-then-ratio catches ~80% of series in under 20 seconds.

3. The six pattern families

The fractional-multiplier tell: decimals like 13.5, 20.25 almost always mean a ×1.5 (or ×0.5, ×2.5) rule — the moment you see a .5 or .25, test a fractional ratio first.

$\text{diagnose gaps}\to \text{if not, ratio}\to \text{if not, }\times n\pm k\text{ or squares/cubes}$

4. The ×n ± k pattern (IBPS's favourite)

When gaps neither stay constant nor form a clean AP, test a_{next} = a \times n \pm k:

• 2, 5, 11, 23, 47 → each is ×2 + 1. Check: 2×2+1=5, 5×2+1=11, 11×2+1=23 ✓.
• The multiplier and the increment often change together: 3, 5, 12, 38, 154 uses ×1+2, ×2+2, ×3+2, ×4+2 — a changing multiplier with a constant add. When a plain ×n±k fails, try letting n increase each step (×2, ×3, ×4…).

This "increasing multiplier" family is where most wrong-term traps live.

5. Wrong-term series

Same diagnosis, one extra move: once you've found the rule from the first two or three secure terms, generate the series yourself and compare. The first term that disagrees with your generated value is the wrong one.

• 3, 5, 12, 38, 154, 809 with rule ×1+2, ×2+2, ×3+2, ×4+2, ×5+2: 3→5→12→38→154→772. The given 809 ≠ 772 ⇒ 809 is wrong.
• Build from the start, not the end — the early terms are usually correct and anchor the rule.

7. The 20-second protocol

For every series:

1. Write the gaps between consecutive terms — is it constant, an AP, or growing?
2. If gaps fail, test the ratio (watch for .5/.25 → fractional multiplier).
3. Still stuck? Try ×n ± k, first with constant n, then with an increasing n.
4. Check squares/cubes (±1, ±2) if terms sit near perfect powers.
5. Wrong-term: lock the rule from the first 2–3 terms, generate forward, flag the first mismatch.
6. Cap at ~30 seconds — if no family fits, mark-and-move; don't let one series eat a DI set's time.