Question

Fifth term of G.P. is $2$, then the product of its nine term is

• A. 256
• B. 512
• C. 1024
• D. None of these

Answer 1

The correct option is B 512

Given $T_5=A{R}^4=2$
where A is the first term and R the common ratio of the G.P
The product of first 9 terms of this G.P is
$A.AR.A{R}^2.A{R}^3......A{R}^8=A^9{R}^{(1+2+3+....+8)}=A^9{R}^{36}={\left(A{R}^4\right)}^9$
$\Rightarrow {\left(A{R}^4\right)}^9=2^9=512$