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Question
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
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Solution
Here, a5 = 2
\[\Rightarrow a r^4 = 2\]
Product of the nine terms, i.e.
\[a, ar, a r^2 , a r^3 , a r^4 , a r^5 , a r^6 , a r^7 \text { and } a r^8\]
\[\left( a \times a r^8 \right)\left( ar \times a r^7 \right)\left( a r^2 \times a r^6 \right)\left( a r^3 \times a r^5 \right)\left( a r^4 \right) = \left( a r^4 \right)^9 \]
\[ \because a r^4 = 2\]
\[\text { Required product } = 2^9 = 512\]
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