Reference no: EM131585274

Question: 1. The first two terms of the Fibonacci sequence are 1, 1. Find two other integers that, together with the recurrence a_n = a_n-1 + a_n-2, do not generate Fibonacci numbers. And, find two other integers that, together with the recurrence an = an-1 +a_n-2, do generate Fibonacci numbers. What kinds of integers do this?

2. Consider the sequence 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176,... . Find both a recurrence and a closed form for this sequence.

3. Find a closed form for a₀ = -1, a₁ = 1, an = 2a_n-1 -a_n-2.