If the n^{th} term of a sequence is \frac{2n+5}{7} then what is the sum of its first 140 terms?

Explanation

The sequence is an arithmetic progression (AP) with first term a = \frac{2(1)+5}{7} = 1 and 140^{th} term l = \frac{2(140)+5}{7} = \frac{285}{7}. The sum is S_{140} = \frac{n}{2}(a + l) = \frac{140}{2}(1 + \frac{285}{7}) = 70(\frac{292}{7}) = 10 \times 292 = 2920.

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