Select the number that can replace the question mark (?). 16, 33, 100, 401, ?

Question

Select the number that can replace the question mark (?). 16, 33, 100, 401, ?

1. A. 525
2. B. 1291
3. C. 1331
4. D. 2006 (Correct answer)

Correct Answer

Option D — 2006

Detailed Solution & Explanation

The correct answer is 2006.

Key Points

• This is a number series where each term is generated by a changing multiply-and-add rule.
• Look at the pattern: 16, 33, 100, 401, ?
• 16 × 2 + 1 = 33
• 33 × 3 + 1 = 100
• 100 × 4 + 1 = 401
• 401 × 5 + 1 = 2006
• The multiplier increases each step (×2, ×3, ×4, ×5) while +1 stays constant, so the next term is 2006.
• when the gaps grow very fast, test a multiplicative rule with an increasing multiplier rather than a fixed difference.
• Verify the rule on every given pair before predicting the missing term.

Exam Tip

• for series that jump sharply (roughly ×2, ×3, ×4…), the pattern is almost always previous × n + constant — check the constant using the first pair.