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

Dear Aparna,

given,

a  = xy^p-1  ,  b = xy^q-1 and c = xy^r-1   here,  x is first term and y is common ratio

as, G² = AH we ahve,

b²=ac

xy^q-1

a^q-r = x^q-r * y^(p-1)(q-r)

b^r-p  = x^r-p * y^(q-1)(r-p)

c^p-q = x^p-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

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.