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Identify any geometric sequences among the following. (a) 1, 4, 9, 16, . . . (b) 1, 4, 7, 10, . . . (c) 1, 4, 16, 64, . . .

Identify any geometric sequences among the following. (a) 1, 4, 9, 16, . . . (b) 1, 4, 7, 10, . . . (c) 1, 4, 16, 64, . . .

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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Identify any geometric sequences among the following.

(a) 1, 4, 9, 16, . . .

(b) 1, 4, 7, 10, . . .

(c) 1, 4, 16, 64, . . .

 

Expert Solution
Step 1

It is known that, for a sequence to be a geometric sequence, there must exist a common ration r such that r=anan-1,  for  n>1

 

Consider the given sequence 1, 4, 9, 16, . . .

Take the ratio of the first two terms,

r1=41=4r2=94Thus r1≠r2

Hence, the given sequence 1, 4, 9, 16, . . . is not a geometric sequence.

 

 

Step 2

Consider the given sequence 1, 4, 7, 10, . . .

Take the ratio of the first two terms,

r1=41=4r2=74Thus r1≠r2

Hence, the given sequence1, 4, 7, 10, . . . is not a geometric sequence.

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