A geometric series, $G$, has common ratio $r$, $r
e 1$, and an arithmetic series, $A$, has a non-ze

Question

A geometric series, $G$, has common ratio $r$, $r
e 1$, 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. Show that $2{{r}^{2}}-3r+1=0$. [2] Deduce that $G$ is convergent. [2] Find the sum to infinity of the even-numbered terms of $G$ in terms of $a$. [2]

Accepted Answer

(i) $2r^2-3r+1=0$; (ii) $G$ is convergent; (iii) $\frac83a$

ASRJC APGP Tutorial Q2

ASRJC APGP Tutorial Q2

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