Question

prove that a1-3a2+3a3-a4 = 0 if a1 a2 a3are in AP.

Answer 1

I don't know if this is correct or not but here goes.... By bringing 3a2 and 3a3 to rhs of equation, We have to prove that a4-a1=3a3-3a2 Lhs = a4-a1 = a+3d-a = 3d Rhs=3a3-3a2 = 3(a3-a2) = 3d Lhs=Rhs Thus proved(I think:))