Question

The fifth term of a G.P. is $1875$. If the first term is $3$, find the common ratio

Answer 1

It is given that the first term of the G.P is $a=3$ and also the $5$th term is $T_5=1875$.

We know that the general term of an geometric progression with first term $a$ and common ratio $r$ is $T_n=a{r}^{n-1}$, therefore,

$T_5=a{r}^{5-1}=a{r}^4$

Now substitute $a=3,n=5$ and $T_5=1875$ in$T_5=a{r}^4$ as follows:

$T_5=a{r}^4\Rightarrow 1875=3r^4\Rightarrow r^4=\frac{1875}{3}\Rightarrow r^4=625\Rightarrow r^4=5^4\Rightarrow r=5$

Hence the common ratio is $5$.