If pth, qth and rth term of an A.P. are a,b,c respectively, then show

1.	If pth, qth and rth term of an A.P. are a,b,c respectively, then show than a(q - r) + b( - p) + c(p - q) = 0.
Answer» ap = a => A + (p - 1) D = a ......(1) aq = b => A + (q - 1) D = b .....(2) ar = c => A + (r + 1) D = c ......(3) Now, L.H.S. = a (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) = 0. R.H.S

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

Answer»

ap = a => A + (p - 1) D = a ......(1)

aq = b => A + (q - 1) D = b .....(2)

ar = c => A + (r + 1) D = c ......(3)

Now, L.H.S. = a (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)

= 0. R.H.S