Question

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

• A. $11$
• B. $10$
• C. $9$
• D. $4$

Hint:

For GP, $T_n = ar^{n-1}$. Sign depends on whether $n-1$ is even/odd.

Answer 1

The Correct Option is A

Step 1: $a=5$, $r=-\frac{1}{2}$. $T_n = 5\left(-\frac{1}{2}\right)^{n-1} = \frac{5}{1024}$.}
Step 2: $\left(-\frac{1}{2}\right)^{n-1} = \frac{1}{1024} = \left(\frac{1}{2}\right)^{10}$. Since RHS positive, $n-1$ even $\Rightarrow n-1=10 \Rightarrow n=11$.}
Step 3: Final Answer: $n=11$.}