Multiplying x2 - ax + b = 0 by xn−1, we get xn+1 - axn + bxn−1 = 0 ...(i) a, p are roots of x2 - ax + b = 0, therefore they will satisfy (i). Also, αn+1 - aαn + bαn−1 = 0 ...(ii) and βn+1 - aβn + bβn−1 = 0 ...(iii) On adding eqs. (ii) and (iii), we get (αn+1+βn+1) - a(αn+βn) + b(αn−1+βn−1) = 0 ⇒ Vn+1 - aVn+bVn−1 = 0 (since n+βn=Vn) Vn+1 = aVn−bVn−1