Question

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

• A. $11$
• B. $10$
• C. $9$
• D. $4$

Answer 1

Answer: (A)

$11$

From given GP, we have

$a=5,r=-\frac{1}{2},a_n=\frac{5}{1024}$

Thus, we have

$\frac{5}{1024}=5{\left(-\frac{1}{2}\right)}^{n-1}\frac{1}{1024}={\left(-\frac{1}{2}\right)}^{n-1}n-1=10n=11$