What comes next: 2, 3, 10, 15, 26, 35, ?

Correct — A.
Rule: n² + 1 and n² − 1 in turn, for n = 1, 2, 3 …

1² + 1 = 2, 2² − 1 = 3
3² + 1 = 10, 4² − 1 = 15
5² + 1 = 26, 6² − 1 = 35
7² + 1 = 50 → option (a).

Why the others are wrong

• (b)
  57 — 57 is 8 more than 7² = 49. Every term in the series sits exactly 1 away from a square, and 57 does not.
• (c)
  47 — 47 is 2 below 7² = 49. The series never moves more than 1 off a square, and with n = 7, odd, the step is +1.
• (d)
  49 — 49 is 7² itself with the ±1 dropped. Odd n takes +1 (1² + 1 = 2, 3² + 1 = 10), so the seventh term is 50.

When a series climbs unevenly, test it against the squares 1, 4, 9, 16, 25, 36, 49. Here every term is one away from a square, alternately above and below.

The differences confirm it. 1, 7, 5, 11, 9 split into two strands, 1, 5, 9 and 7, 11, each rising by 4. The next difference belongs to the 7, 11 strand, so it is 15, and 35 + 15 = 50.

Key facts

• Squares from 1² to 7²: 1, 4, 9, 16, 25, 36, 49.
• Terms here: 1² + 1, 2² − 1, 3² + 1, 4² − 1, 5² + 1, 6² − 1, so the next is 7² + 1 = 50.
• The differences 1, 7, 5, 11, 9, 15 form two strands, each rising by 4.

Common traps

• Spotting 7² = 49 and forgetting the +1
• Reading the differences 1, 7, 5, 11, 9 as random and guessing from the options

No directly related past PYQ was found.