Sequences and Series — Maths STD 11 Science — Question

$\begin{array}{ll} & t_n=a r^{n-1} \\ \therefore \quad & 5^{10}=5 \times 5^{(n-1)} \\ \therefore \quad & 5^{10}=5^{(1+n-1)}\end{array}$

$\begin{array}{ll}\therefore & 5^{10}=5^n \\ \therefore & n=10\end{array}$

$\therefore \quad n=10$

$\therefore \quad 5^{10}$ is the $10^{\text {th }}$ term of the G.P.

Alternate Method:

$\begin{aligned} & t_1=5, t_2=25=5^2, t_3=125=5^3, t_4=625=5^4, \\ \therefore \quad & t_{10}=5^{10}\end{aligned}$