Question

Find the ${10}^{th}$ and $n^{th}$ terms of the G.P. $5,25,125,...$

Answer 1

Given: G.P $5,25,125,....$

Here, first term $a=5$,
and commom ratio $r=\frac{25}{5}=5$
We know, $n^{th}$ term of G.P is given by
$a_n=a{r}^{n-1}$
$\Rightarrow a_n=5(5{)}^{n-1}$
$\Rightarrow a_n=5^{1+n-1}$
$\therefore a_n=5^n\cdots \left(i\right)$

For ${10}^{th}$ term of G.P. Put $n=10$ in equation $\left(i\right)$
$\therefore a_{10}=5^{10}$

Hence, $n^{th}$ term of G.P is $5^n$
And ${10}^{th}$ term of G.P. is $5^{10}$