Answer
a. $-6n+8$
b. $-172$
c. $-2550$
Work Step by Step
a. Based on the given sequence, we have
$a_1=2, d=-4-2=-6$
Thus
$a_n=a_1+(n-1)d=2-6(n-1)=-6n+8$
b. For $n=30$, we have $a_{30}=-6(30)+8=-172$
c. For the sum, we have
$S_n=\frac{n(a_1+a_n)}{2}$
and
$a_{30}=\frac{30(2-172)}{2}=-2550$
