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In a finite G.P. the product of the term...

In a finite G.P. the product of the terms equidistant from the beginning and the end is always same and equal to the product of first and last term.

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Let a be the first term , b the last term and r be the common ratio of the G.P.
Now . ` n^(th)` term of G.P. from beginning = ` ar^(n - 1)` …(i)
From the end , first term is b and common ratio is `(1)/(r)`
` therefore n^(th)` term of G.P. from the end = `b((1)/(r))^(n-1) = (b)/(r^(n-1))` ...(ii)
from (i) and (ii) , ` (n^(th)` term from beginning ) `xx(n^(th)` term from the end ) = `ar^(n-underline1) xx(b)/(r^(n-1))`
ab
= (first term ) `xx` (last term)
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