The series given below contains a sequence of numbers. Accordingly identify the incorrect combination.4, 9, 12, 12, 36, 16, 108 , 18 , 323 , 21

Correct — C.
Rule: two series alternate: odd places × 3, even places + 3.

Odd places: 4, 12, 36, 108, ?
108 × 3 = 324, but the series prints 323.
Even places: 9, 12, ?, 18, 21
12 + 3 = 15, but the series prints 16.

The wrong pair is 16 and 323 → option (c).

Why the others are wrong

• (a)
  18, 323 — 323 is wrong, but 18 is not: the even places run 9, 12, 15, 18, 21, and 18 sits exactly where + 3 puts it.
• (b)
  36 16 — 16 is wrong, but 36 is not: 12 × 3 = 36 on the odd places.
• (d)
  36, 108 — 36 and 108 both fit × 3: 12 × 3 = 36 and 36 × 3 = 108. Neither is a wrong term.

When a series zig-zags (small, big, small, big), split it into two series on alternate places and solve each one alone.

Here the odd places grow fast (× 3) and the even places slowly (+ 3). Each sub-series has one term that breaks its rule, so the 'incorrect combination' is a pair: one wrong term from each.

Confirm by correcting both: 4, 9, 12, 12, 36, 15, 108, 18, 324, 21 is then regular throughout.

Key facts

• Odd places: 4, 12, 36, 108, 324, each × 3.
• Even places: 9, 12, 15, 18, 21, each + 3.
• 323 should be 324, and 16 should be 15.

Common traps

• Spotting 323 at once (its digits sum to 8, so it is not a multiple of 3) and taking the first option that contains it, which pairs it with the correct 18.

No directly related past PYQ was found.