If the `p^(t h)`,`q^(t h)`and `r^(t h)`terms of a GP are a, b and c, respectively. Prove that `a^(q-r)b^(r-p)c^(p-q)=1`.

Explanation

Let A be the first term and R be the common ratio of G.P.
`AR^(p-1)=a`
` AR^(q-1)=b`
`AR^(r-1)=c`
`a^(q-r) b^(r-p) c^(p-q)`
`=A^(q-r) times R^((p-1)(q-r)) times A^(r-p) times R^((q-1)(r-p)) times A^(p-q) times R^((r-1)(p-q))`
`=A^(q-r+r-p+p-q) times R^{(pr-pr-q+r)+(rq-r+p-pq)+(pr-p-qr+p)}`
`=A times 0 times R times 0`
`=1`