Complete the series. 3, 5, 10, 12, 24, 26, ?

Correct — A.
Rule: +2, ×2, +2, ×2 … (the two steps alternate).

3 + 2 = 5
5 × 2 = 10
10 + 2 = 12
12 × 2 = 24

24 + 2 = 26
26 × 2 = 52 → option (a).

Why the others are wrong

• (b)
  54 — 54 is 26 × 2 + 2: it doubles and adds 2 in one step. The +2 was already used on 24 → 26, so this step is ×2 alone.
• (c)
  53 — 53 is odd, but doubling always gives an even number. 26 × 2 is 52, so 53 cannot come from the ×2 step.
• (d)
  50 — 50 adds the last two terms, 24 + 26. That rule fails earlier in the series: 10 + 12 would give 22, not the printed 24.

An alternating series applies two operations in turn. Here they are +2 and ×2: 3 → 5 → 10 → 12 → 24 → 26.

Find the pattern by writing the step between each pair of terms. When the gaps (2, 5, 2, 12, 2) look irregular, try ratios as well: 5 → 10 and 12 → 24 are exact doublings. The seventh term follows a +2, so it takes ×2.

Key facts

• The steps alternate: +2, ×2, +2, ×2, +2, ×2.
• 26 × 2 = 52.
• A +2 followed by ×2 turns x into 2x + 4, which gives 3 → 10 → 24 → 52.

Common traps

• Doubling and adding 2 in the same step, which gives 54
• Adding the last two terms, which gives 50 and already fails at 10 + 12 = 22

No directly related past PYQ was found.