Question

If the $n$th term of the geometric progression, $5,-\frac{5}{2},\frac{5}{4},-\frac{5}{8},\dots$ is $\frac{5}{1024}$, then the value of $n$ is

• A. 11
• B. 10
• C. 9
• D. 4

Answer 1

Answer: (A)

According to the question,
$5{\left(-\frac{1}{2}\right)}^{n-1}=\frac{5}{1024}$
$\Rightarrow {\left(-\frac{1}{2}\right)}^{n-1}={\left(\frac{1}{2}\right)}^{10}$
$\Rightarrow n-1=10$
$\Rightarrow n=11$