Question

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

Answer 1

Given, $a=7$, $t_n=448$ and $S_n=889$
Since, $t_n=a{r}^{n-1}$
$\Rightarrow 448=7r^{n-1}$
$\Rightarrow 7r^n=448r$
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, $t_5=a{r}^4=7{\left(2\right)}^4=112$