Complete the series: __________, 150, 183, 219, 258

Correct — A.
Rule: the gaps grow by 3: 30, 33, 36, 39.

183 − 150 = 33
219 − 183 = 36
258 − 219 = 39

The gap before 150 is 33 − 3 = 30.
First term = 150 − 30 = 120 → option (a).

Why the others are wrong

• (b)
  148 — 148 gives a first gap of only 2 before 150. The gaps rise 33, 36, 39 in threes, so the one before 33 must be 30.
• (c)
  361 — 361 is larger than 150, so the series would fall before it rises. Every step here is an increase, so the missing first term must be smaller than 150.
• (d)
  247 — 247 is also larger than 150, which would make the first step a drop of 97. The series only climbs, by gaps of 30, 33, 36, 39.

When the terms of a number series rise by uneven amounts, write down the differences between neighbours. Here they form their own simple series, 33, 36, 39, climbing by 3.

With the blank at the start, run that pattern backwards. The difference before 33 is 30, so the first term sits 30 below 150. Checking forward, 120 + 30 = 150 fits the chain.

Key facts

• The gaps 30, 33, 36, 39 form an arithmetic series with common difference 3.
• For a blank at the start, reverse the pattern: subtract the earlier gap from the first known term.
• Constant second differences (here 3) mean the terms follow a quadratic pattern.

Common traps

• Adding the gap to 150 instead of subtracting it, because the blank is at the start
• Picking a value close to 150, such as 148, without testing the gap pattern

No directly related past PYQ was found.