A geometric sequence is a sequence in which each term is the same multiple r of the previous term. (a) Give four different examples of a geometric sequence. For each one, make the first term equal to 1 but use a different value of r. Make sure you vary your choices of r to be wildly different kinds of numbers. (b) There are infinitely many possible choices for r. Which value(s) of r will result in a sequence that converges? Explain your reasoning.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
A geometric sequence is a sequence in which each term is the same multiple r of the
previous term.
(a) Give four different examples of a geometric sequence. For each one, make the first
term equal to 1 but use a different value of r. Make sure you vary your choices of r
to be wildly different kinds of numbers.
(b) There are infinitely many possible choices for r. Which value(s) of r will result in a
sequence that converges? Explain your reasoning.
Transcribed Image Text:A geometric sequence is a sequence in which each term is the same multiple r of the previous term. (a) Give four different examples of a geometric sequence. For each one, make the first term equal to 1 but use a different value of r. Make sure you vary your choices of r to be wildly different kinds of numbers. (b) There are infinitely many possible choices for r. Which value(s) of r will result in a sequence that converges? Explain your reasoning.
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