For the G.P. : if a=7 243 , r=1 3 , find t_3. - Vidyadip

Question

For the G.P. : if $\mathrm{a}=\frac{7}{243}, \mathrm{r}=\frac{1}{3}$, find $\mathrm{t}_3$.

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Answer

Given, $\mathrm{a}=\frac{7}{243}, \mathrm{r}=\frac{1}{3}$
$
\begin{aligned}
\mathrm{t}_{\mathrm{n}} & =\mathrm{ar}^{\mathrm{n}-1} \\
\mathrm{t}_3=\frac{7}{243} \times\left(\frac{1}{3}\right)^{3-1} & =\frac{7}{243} \times\left(\frac{1}{3}\right)^2 \\
& =\frac{7}{243} \times \frac{1}{9}=\frac{7}{2187}
\end{aligned}
$

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