Question

If the first term of G.P. is $7,$ its $n^{th}$ term is $448$ and sum of first n terms is $889,$ then find the fifth term of G.P.

Answer 1

Given $a=7$
$t_{n}a{r}^{n-1}=7{\left(r\right)}^{n-1}=448.$
$\Rightarrow$ $7r^n=448r$
Also $S_n=\frac{a(r^n-1)}{r-1}=\frac{7(r^n-1)}{r-1}$
$\Rightarrow$ $889=\frac{448r-7}{r-1}\Rightarrow r=2$
Hence $T_5=a{r}^4=7{\left(2\right)}^4=112.$