Fifth term of a GP is 2, then the product of its 9 terms is

Fifth term of a GP is 2, then the product of its 9 terms is
  1. 256
  2. 512
  3. 1024
  4. none of these

Solution

$\operatorname{ar}^4=2$ $\mathrm{a} \times \operatorname{ar} \times \mathrm{ar}^2 \times a r^3 \times \mathrm{ar}^4 \times \mathrm{ar}^5 \times a r^6 \times a r^7 \times a r^8$ $=a^9 r^{36}=\left(\operatorname{ar}^4\right)^9=2^9=512$

Asked in: JEE Main 2002

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