Suppose that f0, f1, f2,... is a sequence defined as follows: f0 = 5, f1 = 16 fk = 7 fk1

Chapter 5, Problem 6

(choose chapter or problem)

Suppose that \(f_{0}, f_{1}, f_{2}\), . . . is a sequence defined as follows:

\(f_{0} = 5, f_{1} = 16\)

\(f_{k} = 7 f_{k−1} − 10 f_{k−2}\) for all integers k ≥ 2.

Prove that \(f_{n} = 3 \cdot 2^{n} + 2 \cdot 5^{n}\) for all integers n ≥ 0.

Text Transcription:

f_0, f_1, f_2

f_0 = 5, f_1 = 16

f_k = 7 f_k−1 − 10 f_k−2

f_n = 3 cdot 2^n + 2 cdot 5^n