Question

Find the number of terms of a $G.P$ whose first term is $\frac{3}{4},$ common ratio is $2$ and the last term is $384$.

Answer 1

Let first term be $a=\frac{3}{4}$,

And common ratio be $r=2$

$nth$ term $=a{r}^{n-1}=384$

$⟹\frac{3}{4}(2{)}^{n-1}=384$

$⟹(2{)}^{n-1}=512$

$⟹(2{)}^{n-1}=(2{)}^9$

$⟹n=10$

Hence $10$ number of terms.