SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · General Intelligence and Reasoning · Question 4 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

What will be come at the place of question mark? 1, 2, 5, 26, 677, ?

(a)458330
(b)456976
(c)453625
(d)458329

Answer

Why

Correct — A.
Rule: next term = (previous term)² + 1.

1² + 1 = 2, 2² + 1 = 5.
5² + 1 = 26, 26² + 1 = 677.

677² = (700 − 23)²
= 490000 − 32200 + 529 = 458329
458329 + 1 = 458330 → option (a).

Why the others are wrong

(b)
456976 — 456976 is 676², the square of 26² taken before its + 1. The rule squares the whole previous term, 677.
(c)
453625 — 453625 ends in 5. A number ending in 7 squares to one ending in 9, so 677² + 1 must end in 0.
(d)
458329 — 458329 is 677² itself. It stops a step short: the rule adds 1 after squaring.

Concept

Here each term is built from the term before it, not from its position. Square the last term, add 1, and that is the next one.

The numbers grow very fast, so the last step needs care. Split 677 into 700 − 23, or check the units digit first: 7² ends in 9, so 677² + 1 ends in 0.

Of the four options, 458330 alone ends in 0, so the units-digit check settles the answer before any long multiplication.

Key facts

The series is x → x² + 1: 1, 2, 5, 26, 677, 458330.
677² = 458329 and 676² = 456976.
The square of a number ending in 7 ends in 9.

Study next

Series where each term is the previous term times a rising number, plus 1Units-digit shortcuts for squares and cubesSeries of n² + 1 built on the term's position

Common traps

Stopping at 677² and choosing 458329 without adding 1
Squaring 676 instead of 677 and choosing 456976

09 Sep 2024, 09:00, Reasoning Q.25 also builds each term from the one before: 1, 3, 10, 41, ?, 1237 runs ×2 + 1, ×3 + 1, ×4 + 1, and 206 is keyed.

12 Sep 2025, 16:00, Reasoning Q.5 squares the position instead: 2, 5, 10, 17 is n² + 1.

Related PYQs

No directly related past PYQ was found.

Topic: Number Series — all 112 SSC CGL questions on it, every solved shift.