Question 0109

The first, third and fourth terms of a sequence are given by ${u_1 = 15,}$ ${u_3 = 17,}$ ${u_4 = 20.}$ Given that ${u_n}$ is a quadratic polynomial in ${n,}$ find ${u_n}$ in terms of ${n.}$

Find the set of value of ${n}$ for which ${u_n}$ is greater than ${100.}$