Answer
$S_{30}=-3180$
Work Step by Step
RECALL:
The sum of the first $n$ terms ($S_n$) of an arithmetic sequence is given by the formula:
$S_n=\dfrac{n}{2}\left[2a+(n-1)d\right]$
where
$a$ = first term
$d$ = common difference
The given arithmetic sequence has:
$a=10
\\d=-8$
Thus, to find the sum of the first 30 terms, substitute the given values to the formula above to obtain:
$S_n=\dfrac{n}{2}[2a+(n-1)d]
\\S_{30}=\dfrac{30}{2}[2(10) + (30-1)(-8)]
\\S_{30}=15[20+29(-8)]
\\S_{30}=15[20+(-232)]
\\S_{30}=15(-212)
\\S_{30}=-3180$
