Question

the pth qth rth term of an ap are a, b, c respectively.show that (q-r) a+(r-p) b+(p-q) c=0

Answer 1

see tp= A+ (p-1)d=a -----(1)
tq= A+ (q-1)d=b ------(2)
tr = A+ (r-1)d =c ------(3)

so (1) - (2) = a-b/d = p-q
(2) - (3)= b-c/ d = q- r
(3) - (1) = c-a/d = r-p

therefore, (q-r)a+(r-p)b+(p-q)c
= (b-c/d)a + (c-a/d)b + (a-b/d)c
= ab-ac/d + bc-ab/d + ac - bc/d
= ab- ac+bc- ab+ ac- bc/ d
= o/ d = 0