Find the next number in the series 2, 12, 36, 80, 150, ?

246Correct answerYour answer252Correct answerYour answer256Correct answerYour answer294Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Split each term into a square times the next number: $2 = 1^2 \times 2$ , $12 = 2^2 \times 3$ , $36 = 3^2 \times 4$ , $80 = 4^2 \times 5$ , $150 = 5^2 \times 6$ .
So the 6th term is $6^2 \times 7 = 36 \times 7 = 252$ .
Check with differences: 10, 24, 44, 70 have differences 14, 20, 26 (rising by 6), so the next difference is $70 + 32 = 102$ , and $150 + 102 = 252$ .

Worth noting

246 repeats the second difference 26 instead of raising it to 32, and 294 swaps the roles $(7^2 \times 6)$ . When the numbers grow faster than squares but slower than doubling, try $n^2 \times (n + 1)$ or $n^3 \pm n$ .

Concept: Series of the form n² × (n + 1)
Typical timeTypical: 115 s
Your timeYours: —

The rule this testsNumber series

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Ten questions from Number and Letter Series, at your own pace.

Find the next number in the series 2, 12, 36, 80, 150, ?

Explanation