If a,b,c are respectively the Pth,Qth and Rth terms of G.P show that (q-r) log a + (r-p) log b + (p-q) c = 0.

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)

a^q-r b^r-p c^p-q

 whe we put the value, we get

a^q-r b^r-p c^p-q = 1

Now taking log

(q-r) log a + (r-p) log b + (p-q) c = log 1

(q-r) log a + (r-p) log b + (p-q) c = 0

Hence proved