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Q.
Fifth term of a $ GP $ is $ 2 $ , then the product of its $ 9 $ terms is:
Jharkhand CECEJharkhand CECE 2006
Solution:
$ ar^{4}=2 $ ... (i)
Let $ a $ be the first term and $ r $ be the common ratio, then according to the given condition.
Since, $ a\times ar\times ar^{2}\times ar^{3}\times ar^{4}\times ar^{5} $
$ \times ar^{6}\times ar^{7}\times ar^{8} $
$ =a^{9}r^{36}=(ar^{4})^{9}=2^{9}=512 $