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Question -

If the first and the nth term of a G.P.are a ad b, respectively, and if P isthe product of n terms, prove that P2 =(ab)n.



Answer -

Given, the first termof the G.P is a and the last term is b.

Thus,

The G.P. is aarar2ar3,… arn–1, where r is thecommon ratio.

Then,

b = arn–1 … (1)

P = Product of n terms

= (a) (ar)(ar2) … (arn–1)

= (a × a ×…a)(r × r2 × …rn–1)

an r 1+ 2 +…(n–1)  … (2)

Here, 1, 2, …(n –1) is an A.P.

And, the product of nterms P is given by,

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