Home
Class 8
MATHS
If pth,qth and rth terms of an A.P. are ...

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

Text Solution

Verified by Experts

`a=A+(P-1)D-(1)`
`b=A+(q-1)D-(2)`
`c=A+(r-1)D-(3)`
`a(1-r)+b(r-p)+c(p-q)=0`
LHS
`(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(pq-q-pr+r+2r-r-pq+p+pr-p-qr+q)`
`0+0=0`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

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

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (1) a(q-r)+b(r-p)+c(p-q)=0 (2)(a-b)r+(b-c)p+(c-a)q=0

If the pth, qth and rth terms of an A.P. are a,b,c respectively , then the value of a(q-r) + b(r-p) + c(p-q) is :

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

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

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

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

If the pth, qth and rth terms of an A.P. be x,y,z repsectively, then show that : x(q-r)+y(r-p)+z(p-q)=0

The pth, qth and rth terms of an A.P. are a, b and c respectively. Show that a(q – r) + b(r-p) + c(p – q) = 0

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