CAPF AC 2016 PYQ with Answer — Consider the following sequence: 0, 6, 24, 60, 120, 210. Which one of…

2016 · Q59

Consider the following sequence: 0, 6, 24, 60, 120, 210. Which one of the following numbers will come next in the sequence?

general-mental-abilitynumber-alphabet-series

A240
B290
C336
D504

Explanation

The sequence is n^3 - n for n = 1, 2, 3, ...: 1 - 1 = 0, 8 - 2 = 6, 27 - 3 = 24, 64 - 4 = 60, 125 - 5 = 120, 216 - 6 = 210. The next term is 7^3 - 7 = 343 - 7 = 336. Equivalently, successive differences (6, 18, 36, 60, 90) grow by 12, 18, 24, 30, so the next difference is 126 and 210 + 126 = 336.