What number comes next in the series 2, 6, 12, 20, 30, ?

36Correct answerYour answer40Correct answerYour answer42Correct answerYour answer44Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The differences between consecutive terms are 4, 6, 8 and 10 — rising by 2 each time.
The next difference is therefore 12, giving $30 + 12 = 42$ .
The rule can also be written directly: the terms are $1 \times 2$ , $2 \times 3$ , $3 \times 4$ , $4 \times 5$ , $5 \times 6$ , so the next is $6 \times 7 = 42$ .

Worth noting

When the first differences are not constant, take the differences again. Here they are a constant 2, which is the signature of a rule built on $n(n+1)$ .

Concept: Series with a constant second difference
Typical timeTypical: 65 s
Your timeYours: —

The rule this testsNumber series

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

What number comes next in the series 2, 6, 12, 20, 30, ?

Explanation