Question

Find the sum of the given arithmetic series. 14 + 28 + 42 + 56 + ... + 280

Answer 1

14 + 28 + 42 + 56 + … 280

= 14 (1 + 2 + 3 + 4 + … + 20)

= 14 × 20 × 21 / 2

= 2940

where we use the well-known identity,

$\displaystyle \sum_{i=1}^ni = 1 + 2 + 3 + \cdots + n = \dfrac{n(n+1)}2$