Problem 1. Consider the sequences 2,5,12,29,70,169,408, ... (with a0= 2). a. Describe the rate of growth of this sequence. b. Find a recursive definition for the sequence. c. Find a closed formula for the sequence. d. If you look at the sequence of differences between terms, and then the sequence of second differences, the sequence of third differences, and so on, will you ever get a constant sequence? Explain how you know.