if pth, qth,& rth term of an AP are a,b,c respectively, then show that

1.	if pth, qth,& rth term of an AP are a,b,c respectively, then show that a(q-r)+b(r-p)+c(p-q)
Answer» Let the first term and common difference of the AP be A and Dpth term = a ……… (given)= A + (p – 1)D = a\xa0............(1)qth term = b{tex}\\Rightarrow {/tex}\xa0A + (q - 1) D = b ......... (2)rth term = c .......... Given{tex}\\Rightarrow {/tex}\xa0A + (r - 1) D = c ........ (3)Multiplying equations (1), (2) and (3) by q - r, r - p and p - q respecitvely, we geta(q - r) + b(r - p) + c(p - q)= [A + (p - 1) D] (q - r) + [A + (q - 1)D] (r - p) + [A + (r - 1) D] (p - q)]= A [q - r + r - p + p - q] + D [(p - q)\xa0(q - r) + (q\xa0- 1) (r- p) + (r - 1) (p - q)]= A (0) + D(0)= 0

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