Question

The first and last terms of a G.P. are $5$ and $5120$. If the common ratio is $2$, then $S_n$ is:

• A. $5125$
• B. $10235$
• C. $10240$
• D. none of the above

Answer 1

The correct option is B $10235$

$s=a\times \frac{r^n-1}{r-1}$
$l=a\times r^{n-1}$
$\therefore$ $5120=5\times 2^{n-1}$
$\therefore$ $n=11$
$\therefore$ $s=5\times \frac{2047}{1}$
$\therefore$ $s=10235$