Question

The common ratio of a $G.P$ is $3$ and the last terms is $486$. If the sum is $728$. Find the first term.

Answer 1

$r=3$

$a{r}^{n-1}=486$

$a{3}^{n-1}=486$

$=a\left(3^n/3\right)=486$

$=a\left(3^n\right)=1458$ …………$\left(1\right)$

Sum$=728=a\frac{(3^n-1)}{3-1}$

$\Rightarrow a\left(3^n\right)-a=1456$

$\therefore 1458-1456$

$\Rightarrow a=2$.