Suppose r is a fixed constant and a0, a1, a2 ... is a sequence that satisfies the

Chapter 5, Problem 21

(choose chapter or problem)

Suppose r is a fixed constant and \(a_{0}, a_{1}, a_{2}\) . . . is a sequence that satisfies the recurrence relation \(a_{k} = ra_{k−1}\), for all integers k ≥ 1 and \(a_{0} = a\). Use mathematical induction to prove that \(a_{n} = ar^{n}\) , for all integers n ≥ 0.

Text Transcription:

a_0, a_1, a_2

a_k = ra_k−1

a_0 = a

a_n = ar^n