Answer
(a)
$d=-\frac{8}{9}$
$a_{100}=-78$
(b)
$S_{10}=60$
Work Step by Step
$a=10$ and $a_{10}=2$
(a)
$a_n=a+(n-1)d$
$a_{10}=10+(10-1)d$
$2=10+9d$
$-9d=8$
$d=-\frac{8}{9}$
$a_{100}=10+(100-1)(-\frac{8}{9})=10+99(-\frac{8}{9})=10-88=-78$
(b)
$S_n=n(\frac{a+a_n}{2})$
$S_{10}=10(\frac{10+2}{2})=10(6)=60$
