Question

The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.

Answer 1

Given fourth therm $=a{r}^{4-1}=27$

$\Rightarrow$ $a{r}^3=\mathrm{27....}\left(i\right)$

Sevemth term $=a{r}^{7-1}=729$

$\Rightarrow$ $a{r}^6=\mathrm{729....}\left(ii\right)$

dividing (ii) by (i)

we get $t=3$

Using $r=3$ in (i) we get

$a{\left(3\right)}^2=27$ $\Rightarrow$ $a=\frac{27}{27}=1$

$\therefore$ G.P is $1,3,9,27$