Question

if p,q,r term of AP is a,b and c respectively then prove
a(q-r)+b(r-p)+c(p-q)=0

Answer 1

Answer:

let x be the 1st term and d be the com difference

a = x + (p-1)d

b = x + (q-1)d

c= x + (r -1)d

a - b= (p-q)d

(a-b)/d = p-q

multiply both sides by c

c(a-b)/d = c(p-q)

similarly

b(c-a)/d = b(r-p)

a(b-c)/d = a(q-r)

now add both side

LHS = 0

RHS = a(q-r) + b(r-p) + c(p-q) proved