Question
For the G.P.
If $a=\frac{2}{3}, t_6=162$, find $r$.
If $a=\frac{2}{3}, t_6=162$, find $r$.
$\begin{array}{ll}\therefore & t_n=a r^{n-1} \\ \therefore & t_6=\left(\frac{2}{3}\right)\left(r^{6-1}\right) \\ \therefore & 162=\frac{2}{3} r^5 \\ \therefore & r^5=162 \times \frac{3}{2} \\ \therefore & r^5=3^5 \\ \therefore & r=3\end{array}$
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{(2, 1), (3, 1), (5, 2)}