What will come at the place of question mark? 5, 9, 17, 33, 65, ?

Correct — A.
Rule: double the term, then subtract 1 (× 2 − 1).

5 × 2 − 1 = 9, and 9 × 2 − 1 = 17
17 × 2 − 1 = 33, and 33 × 2 − 1 = 65
Next: 65 × 2 − 1 = 129 → option (a).

Check: the gaps 4, 8, 16, 32 double, so the next gap is 64, and 65 + 64 = 129.

Why the others are wrong

• (b)
  120 — 120 adds 55 to 65. The gaps double (4, 8, 16, 32), so the next gap is 64, not 55.
• (c)
  130 — 130 is 65 × 2 with the − 1 left off. Every earlier step subtracts 1, as 33 × 2 − 1 = 65 shows.
• (d)
  127 — 127 is 128 − 1. The terms are a power of 2 plus 1 (4 + 1, 8 + 1 … 64 + 1), so the next is 128 + 1 = 129.

Gaps that double (4, 8, 16, 32) point to a × 2 rule with a fixed adjustment. Find the adjustment from one step: 5 × 2 = 10, and the next term is 9, so the rule is × 2 − 1.

The same series reads as powers of 2 plus 1: 5 = 4 + 1, 9 = 8 + 1, up to 65 = 64 + 1. All three readings give 129.

Key facts

• Each term is double the one before, minus 1.
• The gaps are 4, 8, 16, 32, and the next gap is 64.
• Each term is a power of 2 plus 1: 4 + 1, 8 + 1, 16 + 1, 32 + 1, 64 + 1.

Common traps

• Doubling 65 and forgetting the − 1, which gives 130
• Reading the terms as a power of 2 minus 1 instead of plus 1, which gives 127

No directly related past PYQ was found.