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2. Consider the sequences 2, 5, 12, 29, 70, 169, 408, ... (with að = 2). (a) Describe the rate of growth of this sequence. (b) Find a recursive definition for the sequence. (c) Find a closed formula for the sequence. (d) If you look at the sequence of differences between terms, and then the sequence of second differences, the sequence of third differences, and so on, will you ever get a constant sequence? Explain how you know.

2. Consider the sequences 2, 5, 12, 29, 70, 169, 408, ... (with að = 2). (a) Describe the rate of growth of this sequence. (b) Find a recursive definition for the sequence. (c) Find a closed formula for the sequence. (d) If you look at the sequence of differences between terms, and then the sequence of second differences, the sequence of third differences, and so on, will you ever get a constant sequence? Explain how you know.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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2. Consider the sequences 2, 5, 12, 29, 70, 169, 408,... (with a = 2). (a) Describe the rate of growth of this sequence. (b) Find a recursive definition for the sequence. (c) Find a closed formula for the sequence. (d) If you look at the sequence of differences between terms, and then the sequence of second differences, the sequence of third differences, and so on, will you ever get a constant sequence? Explain how you know.
Transcribed Image Text:2. Consider the sequences 2, 5, 12, 29, 70, 169, 408,... (with a = 2). (a) Describe the rate of growth of this sequence. (b) Find a recursive definition for the sequence. (c) Find a closed formula for the sequence. (d) If you look at the sequence of differences between terms, and then the sequence of second differences, the sequence of third differences, and so on, will you ever get a constant sequence? Explain how you know.
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