An arithmetic progression and a convergent geometric progression each have first term $\frac { 1 } { 2 }$
The sum of the second terms of the two progressions is $\frac { 1 } { 2 }$
The sum of the third terms of the two progressions is $\frac { 1 } { 8 }$
What is the sum to infinity of the geometric progression?
A - 2
B - 1
C $- \frac { 1 } { 2 }$
D $- \frac { 1 } { 3 }$
E $\frac { 1 } { 3 }$
F $\quad \frac { 1 } { 2 }$
G 1
H 2