Question

Which term of the $G.P.2,1,\frac{1}{2},\frac{1}{4},...$ is $\frac{1}{128}$?

• A. $9^{th}$
• B. $8^{th}$
• C. $7^{th}$
• D. $5^{th}$

Answer 1

Answer: (A)

Here, $a=2$ and common ratio $\left(r\right)=1/2$.
Let the $n^{th}$ term be $\frac{1}{128}$. Then,
$a_n=\frac{1}{128}$
$\Rightarrow a{r}^{n-1}=\frac{1}{128}$
$\Rightarrow 2{\left(\frac{1}{2}\right)}^{n-1}=\frac{1}{128}$
$\Rightarrow {\left(\frac{1}{2}\right)}^{n-1}={\left(\frac{1}{2}\right)}^7$
$\Rightarrow n-2=7$
$\Rightarrow n=9$
Thus, $9^{th}$ term of the given $G.P$. is $\frac{1}{128}$.