Select the number that can replace the question mark (?). 2, 9, 28, 65, ?

Question

Select the number that can replace the question mark (?). 2, 9, 28, 65, ?

1. A. 130
2. B. 100
3. C. 110
4. D. 126 (Correct answer)

Correct Answer

Option D — 126

Detailed Solution & Explanation

The correct answer is 126.

Key Points

• This series follows the pattern (cube of a natural number) + 1.
• Series: 2, 9, 28, 65, ?
• 2 = 1³ + 1 (1 + 1)
• 9 = 2³ + 1 (8 + 1)
• 28 = 3³ + 1 (27 + 1)
• 65 = 4³ + 1 (64 + 1)
• ? = 5³ + 1 = 125 + 1 = 126
• So the missing number is 126.
• many number series are n³ ± constant or n² ± constant.
• When the values jump like 2, 9, 28, 65 (close to 1, 8, 27, 64), suspect a cube pattern and test for a small added constant.

Exam Tip

• keep the first cubes handy — 1, 8, 27, 64, 125, 216 — and check whether each term is 'a cube plus or minus 1'; this single idea cracks a large share of series questions.