Answer
$S_6 = 315$
Work Step by Step
RECALL:
The partial sum $S_n$ (sum of the first $n$ terms) of a geometric sequence is given by the formula:
$S_n=a\left(\dfrac{1-r^n}{1-r}\right), r\ne 1$
where
$a$ = first term
$r$ = common ratio
The given geometric sequence has:
$a=5
\\r=2$
Thus, the sum of the first 6 terms is equal to:
$S_6 =5\left(\dfrac{1-2^6}{1-2}\right)
\\S_6=5\left(\dfrac{1-64}{-1}\right)
\\S_6=5 \left(\dfrac{-63}{-1}\right)
\\S_6=5(63)
\\S_6 = 315$