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  4. If the third term of a GP is p . Then the product of the first 5 terms of the GP is:

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Q. If the third term of a $ GP $ is $ p $ . Then the product of the first $ 5 $ terms of the $ GP $ is:

Jharkhand CECEJharkhand CECE 2005

Solution:

Let the first term and common ratio of a $ GP $ series be $ a $ and $ r $ respectively.
According to the given condition $ ar^{2}=p $ ... (i)
$ \therefore $ $ a\cdot ar\cdot ar^{2}\cdot ar^{3}\cdot ar^{4}=(ar^{2})^{5} =p^{5} $ [from (i)]