The sequence a0, a1, a2, ... is defined by letting a0 = 1, and for integers n > 0, an = a b n 2c + a b 2n 3 c + n.(A) Find a1, a2, a3, a4, a5, a6, a7 and a8.(B) Use part (a) to find the least integer a so that an > 4n for all integers n ≥ a.(C) Prove by strong induction that an > 4n for all integers n ≥ a where a is the integer you chose in part (b).(D) Use part (a) to find the least integer b so that an > 45 for all integers n ≥ b.(E) Prove by strong induction that an > 5n for all integers n ≥ b where b is the integer you chose in part (d).