Variations on a recurring theme:

(b) Examine a0 = 1, a1 = 3, an = 2an1 + 3an2 . Generate some terms of the sequence, conjecture a closed form, and then prove that your closed form is correct.

(c) Now examine a0 = 1,a1 = 1,an = 2an1 +3an2. Generate some terms of the sequence, conjecture a closed form, and then prove that your closed form is correct.

(d) This time, look at a0 = a1 = 2,an = 2an1 +3an2, and conjecture what kind of closed form an might have. Now generate some terms of the sequence, conjecture a closed form, and then prove that your closed form is correct.