Question

Find out the appropriate next number in the series from the options below: 0, 2, 6, 12, 20, 30, 42, ?

• A. 56
• B. 62
• C. 49
• D. 5

Hint:

The differences between consecutive terms increase by 2 each time: 2, 4, 6, 8, 10, 12, then 14.

Answer 1

The Correct Option is A

This can also be solved by spotting a direct formula for the $n$th term instead of using successive differences.
Label the terms as $n = 1, 2, 3, \ldots$ and check the product $n(n-1)$:\[n=1: 1 \times 0 = 0\]\[n=2: 2 \times 1 = 2\]\[n=3: 3 \times 2 = 6\]\[n=4: 4 \times 3 = 12\]\[n=5: 5 \times 4 = 20\]\[n=6: 6 \times 5 = 30\]\[n=7: 7 \times 6 = 42\]This matches every given term exactly, so the general formula for the series is $n(n-1)$.
For the 8th term ($n=8$): $8 \times 7 = 56$.\[\boxed{56}\]