Find the missing number: 25, 49, 81, , 169, 225

Question

Find the missing number:

25, 49, 81, , 169, 225

1. A. 100
2. B. 121 (Correct answer)
3. C. 144
4. D. None of the above

Correct Answer

Option B — 121

Detailed Solution & Explanation

The correct answer is 121.

Key Points

• Each term is a perfect square of consecutive odd numbers: 25 = 5², 49 = 7², 81 = 9², then 169 = 13² and 225 = 15².
• The missing term is therefore 11² = 121.
• Checking the differences confirms it: 24, 32, 40, 48, 56 — an arithmetic progression rising by 8.

Additional Information

• When a series grows quickly, test squares and cubes before computing differences; it is usually faster.
• Squares to have memorised up to at least 25²: 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625.
• The gap between consecutive squares n² and (n+1)² is always 2n + 1, which is why the difference row here rises steadily.