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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

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

Grade:12

2 Answers

Anil Pannikar AskiitiansExpert-IITB
85 Points
10 years ago

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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Askiitians Expert

Anil Pannikar

IIT Bombay

 

 

 

 

Aniket Patra
48 Points
10 years ago

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.

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