The number of ways in which three numbers in arithmetic progression can be selected…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The number of ways in which three numbers in arithmetic progression can be selected from 1,2,3,…,n1,2,3,\ldots,n is (1) (n−12)\binom{n-1}{2}, if nn is even (2) n(n−2)4\frac{n(n-2)}{4}, if nn is even (3) n(n−1)4\frac{n(n-1)}{4}, if nn is odd (4) n(n+1)2\frac{n(n+1)}{2}, if nn is odd

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