Question

The $4^{th}$ term of a G.P. is $16$ and $7^{th}$ term is $128$. Find the first term and common ratio of the series.

Answer 1

Let the first term be $a$ and the common ratio be $r$, then the $n^{th}$ term of the G.P. is given by $a_n=a{r}^{n-1}$. So, we have:

$a{r}^3=16,a{r}^6=128$

$\Rightarrow r^3=8\Rightarrow r=2,a=2$

So, the first term and the common difference are both equal to $2$.