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

Chapter 5, Problem 3

(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.

a. Find C and D so that \(a_{0} = 1\) and \(a_{1} = 3\). What is a2 in this case?

b. Find C and D so that \(a_{0} = 0\) and \(a_{1} = 2\). What is a2 in this case?

Text Transcription:

a_0, a_1, a_2

a_n = C cdot 2^n + D

a_0 = 1

a_1 = 3

a_0 = 0

a_1 = 2