Complete the series. 2, 3, 5, 9, 17, ___

Correct — D.
Rule: each term is twice the previous term, minus 1.

2 × 2 − 1 = 3
3 × 2 − 1 = 5
5 × 2 − 1 = 9
9 × 2 − 1 = 17

Next: 17 × 2 − 1 = 33 → option (d).

Check with the gaps: 1, 2, 4, 8 double each time, so the next gap is 16, and 17 + 16 = 33.

Why the others are wrong

• (a)
  30 — 30 is 17 + 13. The gaps between the terms run 1, 2, 4, 8, so the next gap must be 16, not 13.
• (b)
  31 — 31 is 17 + 14, two short of the answer. The gap after 8 in the doubling run 1, 2, 4, 8 is 16.
• (c)
  32 — 32 is 2⁵ with the +1 dropped. Every term is a power of two plus one (1 + 1, 2 + 1, 4 + 1, 8 + 1, 16 + 1), so the next is 32 + 1.

A series whose gaps double (1, 2, 4, 8 …) can be read three ways, and each checks the others.

Term by term: next = previous × 2 − 1.
By gaps: add 1, 2, 4, 8, then 16.
By formula: each term is 2ⁿ + 1, from 2⁰ + 1 = 2 upward.

All three give 33 here. Use whichever you spot first, and confirm with a second.

Key facts

• 2, 3, 5, 9, 17, 33 follows next = previous × 2 − 1.
• The gaps 1, 2, 4, 8, 16 are powers of two.
• Each term is a power of two plus one: 2⁰ + 1 = 2 up to 2⁵ + 1 = 33.

Common traps

• Seeing the powers of two and writing 32, forgetting the +1 every term carries
• Fixing the rule from the first step alone: 2 → 3 fits both + 1 and × 1.5, so test it on every step

No directly related past PYQ was found.