What comes next: 1, 4, 27, 256, ?
- (a)625
- (b)2195
- (c)312
- (d)3125
Answer
Why
Correct — D.
Rule: each term is n raised to the power n.
1 = 1¹
4 = 2²
27 = 3³
256 = 4⁴
Next term: 5⁵ = 5⁴ × 5
= 625 × 5 = 3125 → option (d).
Why the others are wrong
- (a)625 — 625 is 5⁴. It raises the next base to the old exponent, but the rule raises both, so the next term is 5⁵, five times larger.
- (b)2195 — 2195 is not a power of 5 at all: it falls between 5⁴ = 625 and 5⁵ = 3125. No nⁿ value lands there.
- (c)312 — 312 is 3125 with its last digit dropped. 5⁵ must end in 5, as every power of 5 does.
Concept
The jumps are too big for squares (1, 4, 9, 16), so test the terms as powers with a rising exponent. 4 = 2², 27 = 3³ and 256 = 4⁴ show the base and the exponent rising together.
Write each term as nⁿ and the next is 5⁵. One quick check: every power of 5 ends in 5, which rules out 312 at a glance.
256 can also be written as 16² or 2⁸. Only 4⁴ continues the base-equals-exponent pattern set by 1¹, 2² and 3³.
Key facts
- nⁿ for n = 1 to 5: 1, 4, 27, 256, 3125.
- 5⁴ = 625 and 5⁵ = 3125.
- Every positive whole-number power of 5 ends in the digit 5.
Study next
Common traps
- Choosing 625 by raising 5 to the old exponent 4
- Reading 256 as 16² and looking for a square series
14 Sep 2025, 09:00, Reasoning Q.18 fixes the exponent at 2: 1, 4, 9, 16, ?, 36 is keyed 25.
21 Sep 2025, 16:00, Reasoning Q.15 fixes it at 3 and subtracts 1: 0, 7, 26, 63, ? is keyed 124 = 5³ − 1.
Related PYQs
No directly related past PYQ was found.