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

Question

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

1. A. 458330 (Correct answer)
2. B. 456976
3. C. 453625
4. D. 458329

Correct Answer

Option A — 458330

Detailed Solution & Explanation

The correct answer is 458330.

Key Points

• Each term is the square of the previous term, plus 1.
• 1² + 1 = 2, 2² + 1 = 5, 5² + 1 = 26, 26² + 1 = 677.
• So the next term is 677² + 1 = 458,329 + 1 = 458,330.
• Option D (458,329) is 677² without the +1 — the classic trap. Apply the whole rule, not just its first half.
• Series that explode in size are almost always multiplicative or power-based, not additive: check squares, cubes and factorials before hunting for a difference pattern.
• A quick magnitude check confirms it: 677² is around 458,000, so only the two six-digit options are even plausible.

Additional Information

• Recursive series define each term from the previous term rather than from its position — here tₙ = tₙ₋₁² + 1.
• Other recursive forms that recur in SSC: tₙ = tₙ₋₁ × n, tₙ = tₙ₋₁ + n², and the Fibonacci rule tₙ = tₙ₋₁ + tₙ₋₂.
• When terms grow explosively, a magnitude check often settles the answer alone: 677² is roughly 458,000, which eliminates every option not of that size.

प्रश्न (हिन्दी में)

प्रश्नवाचक चिह्न के स्थान पर क्या आएगा? 1, 2, 5, 26, 677, ?

1. A. 458330
2. B. 456976
3. C. 453625
4. D. 458329