Please answer questions

3. The Lucas numbers (lo, (1, . . .) are defined by lo = 2, 61 = 1 and for n 2 2, In = ln-1 + ln-2. Prove that for all n 2 1, In = Fn-1 + Fn+1, where Fr is the kth term in the Fibonacci sequence. 4. Let (ao, a1, ...) be the sequence defined by an = n3. Prove that for all n 21, an = an-1 + 3n- - 3n + 1