For each of the following closed forms write out the first

Question

Question: 1. Write out the first several terms of the integer sequence defined by a₁ = 1, a₂ = 2,a_n = a_n-1 +2a_n-2.

(a) How do things change if you begin with a₁ = 2, a₂ = 1?

(b) What if you begin with a₁ = a₂ = 1?

2. For each of the following closed forms, write out the first several terms of the sequence (at least five) and use this to create a recurrence for the sequence.

(a) a_n = 3n + 1

(b) a_n = 2n + 7

(c) a_n = 3n² + n

(d) a_n = 2^{2n - 1} - 1