Question

If the $2^{nd}$ term of a G.P. is $1$ and $5^{th}$ term is $\frac{1}{125}$, then the $9^{th}$ term will be ____.

• A. $\frac{1}{5^4}$
• B. $\frac{1}{5^7}$
• C. $\frac{1}{5^2}$
• D. $\frac{1}{5^9}$

Answer 1

The correct option is B

$\frac{1}{5^7}$

In a G.P, $T_n$ = $a{r}^{(n-1)}$ [Where a is the first term, r is the common difference and $T_n$ is the $n^{th}$ term ]

$T_2$ = $a{r}^1$ = $1$ .......(i)

and $T_5$ = $a{r}^4$ = $\frac{1}{125}$ .......(ii)

Solving (i) and (ii), we get r = $\frac{1}{5}$ and a = $5$

Now $9^{th}$ term = $a{r}^8$ = $5.\frac{1}{5^8}$ = $\frac{1}{5^7}$