If a, b, c are in A.P. p, q, r are in H.P. and ap, bq, cr are in G.P., thenpr+rp is equal to

According to the given condition   2b=a+c,q=2prp+r and b2q2=(ap)(cr)Substituting values of b and q from first two expressions in the last expression, we get            (a+c)242prp+r2=(ac)(pr)⇒   (a+c)2ac=(p+r)2pr  ⇒  ac+ca=pr+rp