Question

If $6^{th}$ term of $G.P.$ is $2$, then the product of first $11$ terms of the $G.P.$ is equal to

• A. 512
• B. 1024
• C. 2048
• D. 256

Answer 1

Answer: (C)

2048

Answer 2

11 terms of $GP$ are
$\because a r^{5}, a r^{4}, a r^{3}, a r^{2}, a r, a, \frac{a}{r}, \frac{a}{r^{2}}, \frac{a}{r^{3}}, \frac{a}{r^{4}}, \frac{a}{r^{5}}$
6th term of $GP =2$
$\because a=2$
$\therefore$ Product of first 11 terms
$=a r^{5} \times a r^{4} \times a r^{3} \times a r^{2} \times a r \times a \times \frac{a}{r} \times \frac{a}{r^{2}} \times \frac{a}{r^{3}} \times \frac{a}{r^{4}} \times \frac{a}{r^{5}}$
$=a^{11}=2^{11}=2048$