Consider the geometric sequence 7 28 112 448 A common K 12 problem asks students to find a formula a for the nth term beginning with n 1 We wish to prove by induction that an 7 4 1 for each natural number n 1 1 Understand The Question First we must write a recursive definition of the sequence an For the base case a For each k such that ak is defined ak 1 2 The Proof by Induction We proceed by induction on n Note To enter ak type ak