Answer
The sum of first ten terms $S_{10}$ = -2387
Work Step by Step
The given sequence = 7, -14, 28, -56.........
The given sequence is geometric sequence.
Ratio of two consecutive terms
$\frac{-56}{28}$ = - 2
$\frac{28}{-14}$ = - 2
$\frac{-14}{7}$ = - 2
So the common ratio = -2
First term $a_{1}$ = 7
By the formula of the sum of first n terms $S_{n}$ = $a_{1}\frac{(1 - r^{n})}{(1 - r)}$
The sum of first ten terms $S_{10}$ = $7\times\frac{(1 - (-2)^{10})}{(1 - (-2))}$
= $7\times\frac{(1 - 1024)}{(1 + 2)}$
= $7\times\frac{(-1023)}{(32)}$
= $7\times-341$
= -2387
