Question

If fifth term of a G.P. is $2,$ then the product of its first $9$ terms is

• A. $480$
• B. $512$
• C. $627$
• D. $729$

Answer 1

The correct option is B $512$

$t_5=a{r}^4=2$
Product of its first $9$ terms is
$P=a\left(ar\right)\left(a{r}^2\right)\cdots \left(a{r}^8\right)=a^9{r}^{1+2+\cdots +8}$
$=a^9{r}^{36}$
$=(a{r}^4{)}^9=2^9=512$