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

हल

1. 01

   The differences between consecutive terms are 4, 6, 8 and 10 — rising by 2 each time.

2. 02

   The next difference is therefore 12, giving $30 + 12 = 42$.

3. 03

   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 $6 \times 7 = 42$.