The terms of an infinite series $S$ are formed by adding together the corresponding terms in two infinite geometric series, T and U .
The first term of T and the first term of U are each 4. In order, the first three terms of the combined series $S$ are 8,3 , and $\frac { 5 } { 4 }$ What is the sum to infinity of $S$ ?
A $\frac { 32 } { 5 }$ B $\frac { 20 } { 3 }$ C $\frac { 64 } { 5 }$ D $\frac { 40 } { 3 }$ E 16 F 32

The first term of a geometric progression is $2 \sqrt { 3 }$ and the fourth term is $\frac { 9 } { 4 }$ What is the sum to infinity of this geometric progression?
A $- 2 ( 2 - \sqrt { 3 } )$
B $4 ( 2 \sqrt { 3 } - 3 )$
C $\frac { 16 ( 8 \sqrt { 3 } + 9 ) } { 37 }$
D $\frac { 4 ( 2 \sqrt { 3 } - 3 ) } { 7 }$
$\mathbf { E } \frac { 4 ( 2 \sqrt { 3 } + 3 ) } { 7 }$
F $\quad 2 ( 2 + \sqrt { 3 } )$
G $4 ( 2 \sqrt { 3 } + 3 )$

The sum to infinity of a geometric progression is 6 .
The sum to infinity of the squares of each term in the progression is 12 .
Find the sum to infinity of the cubes of each term in the progression.
A 8
B 18
C 24
D $\quad \frac { 216 } { 7 }$
E 72
F 216