#### Answer

$10230$

#### Work Step by Step

$5\times 2^{1} + 5\times 2^{2} + 5\times 2^{3} + ................+ 5\times 2^{10}$
First term $a_{1}= 10$ and common ratio $r = 2$
Sum of the first $n$ terms of Geometric sequence is
$S_{n}= \frac{a_{1}(1-r^{n})}{1-r}$
Substituting $a_{1}= 10, r = 2$ and $n=10$
$S_{n}= \frac{a_{1}(1-r^{n})}{1-r}$
$S_{10}= \frac{10(1-2^{10})}{1-2}$
$S_{10}= \frac{10(1-1024)}{-1}$
$S_{10}= \frac{10(-1023)}{-1}$
$S_{10}= 10230$