Question

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

Answer 1

Here,

$a^2=2$

Nine terms of a G.P. are,

$\frac{a}{r^4},\frac{a}{r^3},\frac{a}{r^2},\frac{a}{r},a,ar,a{r}^2,a{r}^3,a{r}^4$

$\Rightarrow a=2$

Then,

$\frac{a}{r^4}\times \frac{a}{r^3}\times \frac{a}{r^2}\times \frac{a}{r}\times a\times ar\times a{r}^2\times a{r}^3\times a{r}^4$

$=(a{)}^9$

$=(2{)}^9$

$=512$