Geometric Progression

If the pth, qth, rth terms of GP are a , b , c respectively
prove that a^q-rb^r-pc^p-q = 1

How to proceed?

1 Answers

1057

Ketan Chandak ·2012-06-06 00:09:00

let gp's first term be f and common ratio r...

a=fr^p-1
b=fr^q-1
c=fr^r-1

a^q-r=f^q-rr^(p-1)(q-r)
b^r-p=f^r-pr^(q-1)(r-p)
c^p-q=f^p-qr^(r-1)(p-q)

now a^q-rb^r-pc^p-q =
f^{(q-r+r-p+p-q)}r^{(pq-q-pr+r+q-r-p+pq+rp-p+q-rq)}

ultimately all terms in the power cancel out and you are left with nothing but f⁰r⁰ which is 1

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