α and β are the roots of the quadratic equation x2−x−4=0 . ∴α and β are satisfy the given equation. α2−α−4=0 ⇒αn+1−αn−4αn−1=0.......(i) and β2−β−4=0 ⇒βn+1−βn−4βn−1=0⋅⋅⋅⋅⋅⋅⋅(2)Substituting (2) from (1), we get, (αn+1−βn+1)−(αn−βn)−4(αn−1−βn−1)=0 ⇒Pn+1−Pn−4Pn−1=0 ⇒Pn+1=Pn+4Pn−1 ⇒Pn+1−Pn=4Pn−1 For n=14,P15−P14=4P13 For n=15,P16−P15=4P14 Now,