QUESTION 147
In a geometric progression, the first term is 2 and the common ratio is 3. The fifth term of this progression is
(A) 54
(B) 81
(C) 162
(D) 243
(E) 486

In a geometric sequence $\{ a _ { n } \}$, $a _ { 1 } = 1$ and $a _ { 4 } = 4 a _ { 2 }$.
(1) Find the general term formula for $\{ a_n \}$;
(2) Let $S _ { n }$ be the sum of the first $n$ terms of $\{ a_n \}$. If $S _ { m } = 63$, find $m$.

Let the geometric sequence $\left\{ a _ { n } \right\}$ satisfy $a _ { 1 } + a _ { 2 } = 4 , a _ { 3 } - a _ { 1 } = 8$ .
(1) Find the general term formula for $\left\{ a _ { n } \right\}$;
(2) Let $S _ { n }$ be the sum of the first $n$ terms of the sequence $\left\{ \log _ { 3 } a _ { n } \right\}$. If $S _ { m } + S _ { m + 1 } = S _ { m + 3 }$, find $m$ .