Given an AP, if the sum of first 5 terms is 175 and the sum of first 10 terms is 700, find the sum of the first 7 terms.

$\begin{array}{1 1} 14 \\ 7 \\ 343 \\ 49 \end{array}$

$Explanation :\;S_{n}=\frac{n}{2}\;[2a+(n-1)d ]$
$S_{5}=\frac{5}{2}\;[2a+4d]=175$
$10a+20d=350\;------\;(1)$
$S_{10}=\frac{10}{2}\;[2a+9d]=700$
$10a+45d=700\;--------\;(2)$
$sutracting\;(1)\;from(2)$
$10a+45d=700\;----------\;(2)$
$10a+20d=350\;-----------\;(1)$
$25d=350$
$d=\frac{350}{25}=14$
$a=\frac{175-140}{5}=7$
$S_{7}=\frac{7}{2}\;[2*7+(7-1)14]$
$S_{7}=343.$