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