How do you find the sum of the first 25 terms of the sequence: 7,19,31,43...?

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Answer 1 · 2018-07-20T20:15:59

$3775$ $3775$

The given series:

$7, 19, 31, 43, \ldots$

Above series is an arithmetic progression with a common difference

$d=19-7=31-19=43-31=\ldots=12$

First term: $a=7$

The sum of first $n$ terms of an AP with term $a$ & a common difference $d$ is given as

$S_n=n/2(2a+(n-1)d)$

Hence, the sum of first $n=25$ terms of an AP with term $a=7$ & a common difference $d=12$ is given as

$S_{25}=25/2(2\cdot 7+(25-1)12)$

$=3775$