What comes next? 3, 8, 18, 35, 61, ?

Correct — B.
Rule: the differences are n² + 1: 5, 10, 17, 26 …

8 − 3 = 5 = 2² + 1
18 − 8 = 10 = 3² + 1
35 − 18 = 17 = 4² + 1
61 − 35 = 26 = 5² + 1

Next difference: 6² + 1 = 37, so 61 + 37 = 98 → option (b).

Why the others are wrong

• (a)
  88 — 88 adds 27, one more than the last jump of 26. The jumps themselves grow by 5, 7, 9, so the next grows by 11 to 37.
• (c)
  97 — 97 adds 36, which is 6² without the +1. Every jump so far is a square plus one, so the next is 37.
• (d)
  100 — 100 adds 39. The next jump is 6² + 1 = 37, which lands on 98.

When a number series grows unevenly, take the differences between neighbouring terms. If those are not constant, take differences again.

Here the first differences are 5, 10, 17, 26 and the second differences are 5, 7, 9, consecutive odd numbers. Both routes give the same next step: 26 + 11 = 37, which is also 6² + 1. Two independent checks landing on 98 is the confirmation.

Key facts

• First differences: 5, 10, 17, 26, 37.
• Second differences: 5, 7, 9, 11, consecutive odd numbers.
• n² + 1 for n = 2 to 6 gives 5, 10, 17, 26, 37.

Common traps

• Adding 6² = 36 and forgetting the +1, which gives 97

No directly related past PYQ was found.