Answer: Let a0, a1, a2,... be the sequence defined by the explicit formula an = C 2n + D

Chapter 5, Problem 5

(choose chapter or problem)

Let \(a_{0}, a_{1}, a_{2}\), . . . be the sequence defined by the explicit formula

\(a_{n} = C \cdot 2^{n} + D\) for all integers n ≥ 0,

where C and D are real numbers. Show that for any choice of C and D,

\(a_{k} = 3a_{k−1} − 2a_{k−2}\) for all integers k ≥ 2.

Text Transcription:

a_0, a_1, a_2

a_n = C cdot 2^n + D

a_k = 3a_k−1 − 2a_k−2