Sequence and Series - Sum to infinity

The fifth, tenth and twentieth term of a convergent geometric progression, \({G}\), are the first three consecutive terms of an arithmetic progression, \({A}\).

1. Determine the common ratio \({G}\).[3]

Given that the first term of \({G}\) is \({2}\).

2. evaluate the sum to infinity for \({G}\).[2]
3. find the sum of the first \({10}\) odd-numbered terms in \({A}\).[3]