Question

$3^{rd}$ term of a G.P. is $27$ and its $6^{th}$ term is $729$. Find its $7^{th}$ terms.

Answer 1

Given

$3^{rd}$ term of GP$=27$

$6^{th}$ term of GP$=729$

$a{r}^2=27$

$a{r}^5=729$

$\frac{a{r}^5}{a{r}^2}=\frac{729}{27}$

$r^3=\left(\frac{729}{27}\right)$

$r={\left(\frac{9^3}{3^3}\right)}^{\frac{1}{3}}$

$r=3$

$a\times r^2=27$

$a\times 9=27$

$a=3$

$7^{th}$ term $=a{r}^6$

$=3\times 3^6$

$=3\times 729$

$7^{th}$ term $=2187$.