Question

Which term of $G.P.:3,9,27,.....$ is $2187?$

Answer 1

$3,9,27,...2187$ are in G.P

$n^{th}$ term of G.P$=t_n=a{r}^{n-1}$

$a=3,r=\frac{9}{3}=\frac{27}{9}=3$

$\Rightarrow 33^{n-1}=2187$

$\Rightarrow 3^{1+n-1}=2187$

$\Rightarrow 3^n=2187$

$\Rightarrow 3^n=3^7$

Since bases are same, we can equate the powers,

$\therefore n=7$