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Aparna Tiwari Grade: 12
        

If the pth,qth and rth terms of a G.P are a,b,c resp.Pove that:-


(a^(q-r))(b^(r-p))(c^(p-q))=1

6 years ago

Answers : (2)

Anil Pannikar AskiitiansExpert-IITB
85 Points
										

Dear Aparna,


given,


a  = xyp-1  ,  b = xyq-1 and c = xyr-1   here,  x is first term and y is common ratio


as, G2 = AH we ahve,


b2=ac


xyq-1


aq-r = xq-r * y(p-1)(q-r)


br-p  = xr-p * y(q-1)(r-p)


cp-q = xp-q * y(p-q)(r-1)


multiply all 3 of them, we get RHS,


x0 * y0 = 1


henc proved.


 



 



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Anil Pannikar


IIT Bombay


 


 


 


 

6 years ago
Aniket Patra
48 Points
										

Just multiply the terms..and find the pth,qth and rth term by using the formula.(take x as the first term)..And then put the values in the expression..u will get (abc)^0 i.e. 1.

6 years ago
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