Select the number from among the given options that can replace the question mark (?) in the following series. 3, 6, 9, 18, 21, ?

Correct — A.

Rule: the operation alternates, x2 then +3.

3 x 2 = 6
6 + 3 = 9
9 x 2 = 18

18 + 3 = 21
21 x 2 = 42 → option (a)

The doubling steps land on 6, 18 and 42, the additions on 9 and 21, so the term after a +3 must be a doubling.

Why the others are wrong

• (b)
  40 — 40 is neither 21 x 2 nor 21 + 3. No step in the series produces it, and the gaps 3, 3, 9, 3 never settle into a constant that would.
• (c)
  63 — 63 is 21 x 3. The multiplying steps here are x2 — 3 to 6 and 9 to 18 — so tripling contradicts the rule the series has already shown.
• (d)
  24 — 24 is 21 + 3, which repeats the addition instead of alternating. After the earlier +3, from 6 to 9, the series doubled.

Short SSC series rarely hide a single difference. Take differences first: 3, 3, 9, 3.

The moment the differences stop being regular, test a two-operation cycle instead of hunting for a cleverer single rule.

Doubling and adding 3 in turn reproduces every printed term. Both halves of the rule are confirmed by more than one step: 3 to 6 and 9 to 18 are doublings, 6 to 9 and 18 to 21 are additions.

With five terms given, an alternating rule can be checked all the way along before it is applied.

Key facts

• 3, 6, 9, 18, 21 is generated by x2 and +3 applied in turn.
• The differences run 3, 3, 9, 3, which no single arithmetic rule produces.
• The doubling steps give 6, 18 and 42, the addition steps give 9 and 21.

Common traps

• Adding 3 again because two of the first three gaps are 3
• Multiplying by 3 because 3, 6, 9 reads like a times table
• Abandoning the question when the difference test fails instead of trying a second operation

No directly related past PYQ was found.