ASRJC APGP Tutorial Q2

A geometric series, \(G\), has common ratio \(r\), \(r\ne 1\), and an arithmetic series, \(A\), has a non-zero first term \(a\).

The first three terms of \(G\) are equal to the seventh, third and first term of \(A\) respectively.

1. Show that \(2{{r}^{2}}-3r+1=0\).[2]
2. Deduce that \(G\) is convergent.[2]
3. Find the sum to infinity of the even-numbered terms of \(G\) in terms of \(a\).[2]