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

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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 = \frac{n(n+1)}2

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