The common ratio and the fifth term of a $G.P$ are $3$ and $324$ respectively , Find the first term of the $G.P.$
Answer
In the given $G.P...,$ the common ratio $r=3$, the fifth term is $324$ i..e, $T=324$ and we required the first term of the $G.P.$ i.e. a.
Here,$T_5=324$
$\therefore a r^{5-1}=324\left(\therefore T_n=a r^{n-1}\right)$
$\therefore a(3)^4=324(\therefore r=3)$
$\therefore a \times 81=324$
$\therefore a =\frac{ 3 2 4 }{ 8 1 }=4$
Hence, the first term of the $G.P.$ is $4.$