Answer
(a) $-1215$
(b) diverges.
(c) $3$
Work Step by Step
(a) Arithmetic, $a_1=3, a_{30}=-3(30)+6=-84$, $S_{30}=\frac{30}{2}(3-84)=-1215$
(b) Geometric $r=2$, diverges.
(c) Geometric $a_1=\frac{3}{4}, r=\frac{3}{4}$, $S=a_1\times\frac{1}{1-r}=\frac{3}{4}\times\frac{1}{1-\frac{3}{4}}=3$
