Which term is wrong in the series: 2, 5, 10, 17, 26, 36

Correct — C.
Rule: each term is a square plus one, n² + 1.

1² + 1 = 2, 2² + 1 = 5, 3² + 1 = 10
4² + 1 = 17, 5² + 1 = 26
6² + 1 = 37, but the series prints 36

So 36 is the wrong term → option (c).

Why the others are wrong

• (a)
  5 — 5 is 2² + 1, and 5 − 2 = 3 starts the run of odd differences. It fits the rule.
• (b)
  10 — 10 is 3² + 1, and 10 − 5 = 5 continues the odd differences. It fits the rule.
• (d)
  26 — 26 is 5² + 1, and 26 − 17 = 9 keeps the odd differences going. The break comes after it: 36 − 26 = 10, where 11 is due.

Two routes reach the same answer. The differences 3, 5, 7, 9 are consecutive odd numbers, so the next is 11 and the last term should be 26 + 11 = 37.

Read as a formula, the terms are n² + 1: 2, 5, 10, 17, 26, 37. 36 is a perfect square itself, which makes it look at home, but the rule needs one more.

Key facts

• Squares plus one: 2, 5, 10, 17, 26, 37, 50.
• Consecutive terms of n² + 1 differ by the odd numbers 3, 5, 7, 9, 11.
• The correct last term here is 37.

Common traps

• Accepting 36 because it is a perfect square
• Changing an early term instead of the one that breaks the differences

No directly related past PYQ was found.