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If the $5$-th term of the G.P is its middle term and its value is 2,then find the product of all terms of this GP?

My approach:

Since $a_5$ is the middle term, so the GP contains 9 terms.

$$P_9 = a\cdot ar\cdot ar^2 \cdot ar^3 \cdot 2\cdot ar^5 \cdots ar^8$$

which leaves us $P_9 = 2\cdot (ar^4)^8$ ... I am not getting how to proceed further? Is this approach even correct?

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You know what $ar^4$ is! – Blue Dec 5 '10 at 13:25
up vote 4 down vote accepted

The fourth term is $2/r$ and the sixth term is $2r$. What happens when you multiply these? What about the third and seventh terms?

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+1,Thanks that was a sufficient hint :-) – Quixotic Dec 5 '10 at 13:23
So in general, if $X$ is the middle term then the product of the GP is $X^{\text{ no of terms }}$ – Quixotic Dec 5 '10 at 13:24

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