What comes next: 10, 17, 26, 37, 50, ?

Correct — D.
Rule: the gaps grow by 2: +7, +9, +11, +13.

10 + 7 = 17
17 + 9 = 26
26 + 11 = 37
37 + 13 = 50

The next gap is +15: 50 + 15 = 65 → option (d).

Why the others are wrong

• (a)
  45 — 45 is smaller than 50, but every step in the series adds. A rising series whose gaps keep growing cannot fall back.
• (b)
  54 — 54 adds only 4 to 50. The gaps have climbed by 2 each time, from 7 up to 13, so the next one is +15, not +4.
• (c)
  76 — 76 adds 26 to 50, far past the next gap of +15. It fits neither the gaps nor n² + 1, which gives 8² + 1 = 65.

When the gaps in a number series are not equal, write them out and read them as a series of their own.

Here the gaps are 7, 9, 11, 13: odd numbers rising by 2. The next gap is 15, giving 65.

The same series reads as n² + 1: 3² + 1 = 10, 4² + 1 = 17, up to 7² + 1 = 50. Then 8² + 1 = 65, the same answer by a second route.

Key facts

• Consecutive squares differ by consecutive odd numbers: 4² − 3² = 7, 5² − 4² = 9.
• 10, 17, 26, 37, 50, 65 are n² + 1 for n = 3 to 8.
• The n² + 1 series runs 2, 5, 10, 17, 26, 37, 50, 65, 82.

Common traps

• Adding the last gap, +13, again and looking for 63, which is not an option

No directly related past PYQ was found.