Question

The fourth term of a G.P. is 27 and the 7th term is 792, find the G.P.

Answer 1

$t_4=27$

$t_7=729$

We know that $t_n=a{r}^{n-1}$

$t_4=a{r}^3=27$

$t_7=a{r}^6=729$

Now,

$\Rightarrow \frac{t_7}{t_4}=\frac{a{r}^6}{a{r}^3}\Rightarrow r^3=\frac{729}{27}$

$\Rightarrow r^3={\left(\frac{9}{3}\right)}^3$

$r^3=3^3$

$r=3$

Putting r = 3 in $a{r}^3=27$

$a(3{)}^3=27$

$\Rightarrow a=1$

Now G.P is a, ar, ar^2, ...... 1, 3, 9.....