Question

The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.

Answer 1

$r=3,$ last term $\left(a_n\right)$ is 486

Sum of terms $=S_n=728,a=?$

$a_n=486$

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

$\Rightarrow a(3{)}^{n-1}=486$

$\Rightarrow a(3{)}^n=486\times 3$

$\Rightarrow a(3{)}^n=1458$ ..........(i)

Now $S_n=728$

$\Rightarrow 728=a\left(\frac{3^n-1}{3-1}\right)$

$\Rightarrow 728=\left\{\frac{a(3{)}^n-a}{2}\right\}$

$\Rightarrow 1456=a(3{)}^n$

$\Rightarrow 1456=1458-a$ [From (i)]

$\Rightarrow a=2$