Select the number from the given options to complete the series. 35, 38, 43, 50, 59, ___

Correct — B. Rule: the gaps are the consecutive odd numbers +3, +5, +7, +9, +11.

35 to 38 is +3
38 to 43 is +5
43 to 50 is +7
50 to 59 is +9

The next gap has to be +11, so 59 + 11 = 70, option (b).

A second reading lands on the same term: every entry is 34 more than a perfect square. 1+34 = 35, 4+34 = 38, 9+34 = 43, 16+34 = 50, 25+34 = 59 and 36+34 = 70.

Why the others are wrong

• (a)
  68 — 68 needs a gap of +9, which is the gap the series has just used. Each gap here is two more than the one before it.
• (c)
  62 — 62 needs a gap of +3, the very first gap in the run. The gaps only grow, so the series can never fall back to 3.
• (d)
  78 — 78 needs a gap of +19, skipping four gaps at once. It also fails the squares reading, since 78 - 34 = 44 is not a perfect square.

A second-difference series is one whose gaps form a pattern of their own. Write the gaps out once and the answer is usually visible immediately.

Here the gaps are 3, 5, 7, 9 — consecutive odd numbers, rising by a constant 2. A constant second difference is the signature of a quadratic, which is why the terms are also n² + 34.

Either reading is enough on its own. The odd-number gaps are faster under exam pressure, and the squares form is the better check when two options sit close together.

Key facts

• The differences are 3, 5, 7, 9 and 11 — consecutive odd numbers.
• Each term equals n² + 34 for n = 1, 2, 3, 4, 5, 6.
• The completed series is 35, 38, 43, 50, 59, 70.

Common traps

• Reading the gaps correctly as +3, +5, +7, +9 and then adding 9 once more.
• Assuming the gaps double when in fact they rise by a fixed amount.

No directly related past PYQ was found.