Q. 54

#
If the p^{th}, q^{th} and r^{th} terms of a G.P. are a, b, c respectively, prove that a^{q-r} . b^{r-p} . c^{p-q} = 1.

Answer :

Let x be the first term and R the common ratio.

T

_{p}= x R

^{p-1}= a ………(1)

T

_{q}= x R

^{q-1}= b ……….(2)

T

_{r}= x R

^{r-1}= c ………(3)

a

^{q-r}= = ...........(1)

b

^{r-p}= ………….(2)

c

^{p-q}= ……….(3)

L.H.S. = (1) x (2) x (3)

.=1.

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