Select the number from among the given options that can replace the question mark (?) in the following series. 99, 123, 150, 180, 213, ?

Correct — D. The gaps are not constant, so difference the series once.

Rule: first differences 24, 27, 30, 33 — each one 3 more than the last.

123 − 99 = 24
150 − 123 = 27
180 − 150 = 30
213 − 180 = 33

Next difference = 33 + 3 = 36
213 + 36 = 249 → option (d).

Why the others are wrong

• (a)
  248 — 248 is 35 above 213. The difference row advances by exactly 3 each time, so it demands 36, not 35 — this is the answer you reach after one slip in a subtraction.
• (b)
  258 — 258 is 45 above 213. The gap would have to jump 33 → 45, which means adding 12 to the last difference instead of 3.
• (c)
  259 — 259 is 46 above 213. No gap in this series is anywhere near 46; the differences grow slowly and evenly.

When a series does not move by a constant amount, difference it and treat the difference row as a series in its own right.

Here 24, 27, 30, 33 is itself an arithmetic progression with common difference 3. Series built this way are quadratic in the term number, but you never need that formula under exam pressure.

Extend the difference row by one step, then add it back to the last term. That is faster than fitting an expression to five terms, and it goes wrong far less often.

Key facts

• First differences: 123 − 99 = 24, 150 − 123 = 27, 180 − 150 = 30, 213 − 180 = 33.
• Those differences rise by a constant 3, so the next difference is 36.
• 213 + 36 = 249.

Common traps

• Stopping at the difference row and offering 36 itself as the answer instead of adding it back.
• Reading 213 − 180 as 32 and then adding 35, which lands exactly on option (a).
• Hunting for a multiplication rule first — the terms grow far too slowly for that.

No directly related past PYQ was found.