Math 310: Problem set 3

Instructions: This problem set is due Friday, January 27, 2006. Your goal is not only to give correct answers but to communicate your ideas well. Make sure you use good English,
  1. Let f(n) be the sum of the first n natural numbers which are triples plus 1 (i.e., the sum of the first n numbers from the sequence 4, 7, 10, ... .) Thus f(1) = 4, f(2) = 4 + 7, and f(n) = 4 + 7 + ... + (3n+1) for n >= 3.
  2. Let a1 = 3, a2 = 9, and, for integers n > 1, let an+1 = 2an + 3an-1. Use a version of induction to prove for all integers n > 0, that an = 3n.