If the pth, qth and rth terms of a GP be a, b, c respectively, prove that

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

where ^=raised to the power

Let A and R be the first term and common ratio of G.P. respectively.

n th term of G.P., an = AR n – 1

p th term of G.P. = a

∴ AR p – 1 = a ...(1)

q th term of G.P. = b

∴ AR q – 1 = b ...(2)

r th term of G.P. = c

∴ AR r – 1 = c ...(3)

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