If `p^(t h),\ q^(t h),\ a n d\ r^(t h)` terms of an A.P. and G.P. are both `a ,\ b\ a n d\ c` respectively show that `a^(b-c)b^(c-a)c^(a-b)=1.`

Explanation

Let,


`A=` first term


`d=` common difference


`A_p=a=A+(p−1)d=(A−d)+pd`` \ \ \ …(1)`


`A_q=b=A+(q−1)d=(A−d)+qd`` \ \ \ …(2)`


`A_r=c=A+(r−1)d=(A−d)+rd`` \ \ \ …(3)`


We have to eliminate `A` and `d`


Multiply `(1)` by `q-r`, (2) by `r−p`, (3) by `p−q` and adding all equations:


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