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)