For the G.P. : if a=2 3 , t_6=162, find r. - Vidyadip

Question

For the G.P. : if $a=\frac{2}{3}, t_6=162$, find $r$.

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Answer

Given, $\mathrm{a}=\frac{2}{3}, \mathrm{t}_6=162$
$
\begin{array}{ll}
& \mathrm{t}_{\mathrm{n}}=\mathrm{ar}^{\mathrm{n}-1} \\
\therefore & \mathrm{t}_6=\left(\frac{2}{3}\right)\left(\mathrm{r}^{6-1}\right) \\
\therefore & 162=\frac{2}{3} \mathrm{r}^5 \\
\therefore & \mathrm{r}^5=162 \times \frac{3}{2} \\
\therefore & \mathrm{r}^5=3^5 \\
\therefore & \mathrm{r}=3
\end{array}
$

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