If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
The first term of the G.P is a and the last term is b.
Therefore, the G.P. is a, ar, ar2, ar3, … arn–1, where r is the common ratio.
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.
∴1 + 2 + ……….+ (n – 1)
Thus, the given result is proved.
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7 Comment(s) on this Question
Thank you
Very good.. thanks for the easiest way.
Very good
Please change the colour of this page And nice explanation
Why n-1/2 is taken instead of n/2
Change the colour of the page
Good
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