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Is the sequence shown in the picture bounded? Why or why not? What work has to be done to show if a sequence is bounded? I already found that it is an arithmetic sequence and the formula is an= 3n-2

Is the sequence shown in the picture bounded? Why or why not? What work has to be done to show if a sequence is bounded? I already found that it is an arithmetic sequence and the formula is an= 3n-2

Calculus: Early Transcendentals
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...
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Is the sequence shown in the picture bounded? Why or why not? What work has to be done to show if a sequence is bounded?

I already found that it is an arithmetic sequence and the formula is an= 3n-2

{an} = {1,4,7, 10, ...}
Transcribed Image Text:{an} = {1,4,7, 10, ...}
Expert Solution
Step 1

The given sequence is:

an=1,4,7,10,..... 

Given sequence is a arithmetic progression with:

an =a+n-1d                     …..(1)

Here a is the first term, d is the common difference and n is the number of terms.

a=1

d=4-1=3    

Substitute the above values in equation (1)

an=1+n-1 3=1+3n-3=3n-2 

an=3n-2

For n=1

a1=3×1-2=1 

For n=2

a2=3×2-2=4 

For n=3

a3=3×3-2=7  

For n=4

a4=3×4-2=10  

The sequence is increasing for increasing values of n.

The lower bound of the sequence is 1.

limn→∞an=limn→∞3n-2=∞  

The above sequence does not converge, so it is not a bounded sequence

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