Q29. If pth, qth and rth terms of an А.Р. are(a - br (b- op + (c- a)

1.	Q29. If pth, qth and rth terms of an А.Р. are(a - br (b- op + (c- a)4 0.a, b,c respectively, thenshow that
Answer» Let a = first term of the AP.andLet d = common difference of the AP Nowa = A+(p-1).d.......(1)b = A+(q-1).d.......(2)c = A+(r-1).d........(3) Subtracting 2nd from 1st, 3rd from 2nd and 1st from 3rd we get a-b = (p-q).d......(4)b-c = (q-r).d........(5)c-a = (r-p).d.......(6) multiply 4,5,6 by c,a,b respectively we have c.(a-b) = c.(p-q).d......(4)a.(b-c) = a.(q-r).d........(5)b.(c-a) = b.(r-p).d.......(6) a(q-r).d+b(r-p).d+c(p-q).d = 0(a(q-r)+b(r-p)+c(p-q)).d = 0 Now since d is common difference it should be non zero Hencea(q-r)+b(r-p)+c(p-q)= 0

Q29. If pth, qth and rth terms of an А.Р. are(a - br (b- op + (c- a)4 0.a, b,c respectively, thenshow that

Answer»

Let a = first term of the AP.andLet d = common difference of the AP

Nowa = A+(p-1).d.......(1)b = A+(q-1).d.......(2)c = A+(r-1).d........(3)

Subtracting 2nd from 1st, 3rd from 2nd and 1st from 3rd we get

a-b = (p-q).d......(4)b-c = (q-r).d........(5)c-a = (r-p).d.......(6)

multiply 4,5,6 by c,a,b respectively we have

c.(a-b) = c.(p-q).d......(4)a.(b-c) = a.(q-r).d........(5)b.(c-a) = b.(r-p).d.......(6)

a(q-r).d+b(r-p).d+c(p-q).d = 0(a(q-r)+b(r-p)+c(p-q)).d = 0

Now since d is common difference it should be non zero

Hencea(q-r)+b(r-p)+c(p-q)= 0