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Aparna Tiwari Grade: 12
```        If the first and nth terms of a G.P. are a and b resp.and if P is the product of n terms,prove that:-
P^2=(ab)^n```
7 years ago

## Answers : (1)

Anil Pannikar AskiitiansExpert-IITB
85 Points
```										Dear Aparna,

nth term  = arn-1
so,  b = arn-1
and P = a(ar)(ar2)(ar3).......(arn-1)

=an(r.r2.....rn-1)
=an(r1+2+........+n-1)
=an(r)n(n-1)/2
Therefore, P2=a2n(r)n(n-1)
as,  b = arn-1,
P2= an(arn-1)n
i.e. P2=an(b)n
so, P2=(ab)n

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Anil Pannikar
IIT Bombay

```
7 years ago
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