If pth, qth, and rth terms of an A.P. are `a ,b ,c ,` respectively, then show that `(a-b)r+(b-c)p+(c-a)q=0`

Explanation

Let A be the first term and D be the common difference.

pth term `= A+(p-1)D = a`

`a = A-D+pD …(i)`

`qth term = A+(q-1)D = b`

`b = A-D+qD …(ii)`

`rth term = A+(r-1)D = c`

`c = A-D+rD …(iii)`

Multiply (i) , (ii), (iii) by `(q – r), (r – p), (p – q) `respectively and adding them we get
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