Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 8.3, Problem 34E

(a)

To determine

To find: the $9th$ term of the geometric sequence using the table feature of a graphing utility.

(a)

Expert Solution

Answer to Problem 34E

$9th$ term of the geometric sequence is 0.8009.

Explanation of Solution

Given information:

Given geometric sequence

$a1=8,r=−34$

Calculation:

To have the $nth$ term of the geometric sequence, firstly click on $2nd$ button and then click on STAT button. After this, a new screen will appear. The screenshot is given as below:

Precalculus with Limits: A Graphing Approach, Chapter 8.3, Problem 34E , additional homework tip 1

Now, move to the OPS option and then move to the $5th$ option and press the ENTER button. After this, give the input in this function. The pattern of the giving the input. Then finally press the ENTER button to have the desired value. The screenshot is given as below:

Precalculus with Limits: A Graphing Approach, Chapter 8.3, Problem 34E , additional homework tip 2

Therefore, according to the above screenshot, the $9th$ term is 0.8009.

(b)

To determine

To find: the $9th$ term of the geometric sequence algebraically.

(b)

Expert Solution

Answer to Problem 34E

$9th$ term of the geometric sequence is 0.8009.

Explanation of Solution

Concept used:

The $n$ th term of geometric sequence has the form $a1=a1rn−1$ where $r$ is the common ratio of the consecutive terms of the sequence.

Every geometric sequence can be written in the following form.

$a1=a1,a2=a1r,a3=a1r2,a4=a1r3,...,an=a1rn−1,..$

Calculation:

The $9th$ term of this geometric sequence can be calculated by using formula:

$an+1=arn$

So,

$a8+1=8×(−34)8a9=8×656165536a9=52248865536≈0.8009$

Hence, $9th$ term of this geometric sequence is 0.8009.

Chapter 8.3, Problem 33E

Chapter 8.3, Problem 35E

Chapter 8 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Prob. 44RE Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE Ch. 8 - Prob. 59RE Ch. 8 - Prob. 60RE Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Prob. 64RE Ch. 8 - Prob. 65RE Ch. 8 - Prob. 66RE Ch. 8 - Prob. 67RE Ch. 8 - Prob. 68RE Ch. 8 - Prob. 69RE Ch. 8 - Prob. 70RE Ch. 8 - Prob. 71RE Ch. 8 - Prob. 72RE Ch. 8 - Prob. 73RE Ch. 8 - Prob. 74RE Ch. 8 - Prob. 75RE Ch. 8 - Prob. 76RE Ch. 8 - Prob. 77RE Ch. 8 - Prob. 78RE Ch. 8 - Prob. 79RE Ch. 8 - Prob. 80RE Ch. 8 - Prob. 81RE Ch. 8 - Prob. 82RE Ch. 8 - Prob. 83RE Ch. 8 - Prob. 84RE Ch. 8 - Prob. 85RE Ch. 8 - Prob. 86RE Ch. 8 - Prob. 87RE Ch. 8 - Prob. 88RE Ch. 8 - Prob. 89RE Ch. 8 - Prob. 90RE Ch. 8 - Prob. 91RE Ch. 8 - Prob. 92RE Ch. 8 - Prob. 93RE Ch. 8 - Prob. 94RE Ch. 8 - Prob. 95RE Ch. 8 - Prob. 96RE Ch. 8 - Prob. 97RE Ch. 8 - Prob. 98RE Ch. 8 - Prob. 99RE Ch. 8 - Prob. 1CT Ch. 8 - Prob. 2CT Ch. 8 - Prob. 3CT Ch. 8 - Prob. 4CT Ch. 8 - Prob. 5CT Ch. 8 - Prob. 6CT Ch. 8 - Prob. 7CT Ch. 8 - Prob. 8CT Ch. 8 - Prob. 9CT Ch. 8 - Prob. 10CT Ch. 8 - Prob. 11CT Ch. 8 - Prob. 12CT Ch. 8 - Prob. 13CT Ch. 8 - Prob. 14CT Ch. 8 - Prob. 15CT Ch. 8 - Prob. 16CT Ch. 8 - Prob. 17CT Ch. 8 - Prob. 18CT Ch. 8 - Prob. 19CT Ch. 8 - Prob. 20CT Ch. 8 - Prob. 21CT Ch. 8 - Prob. 22CT Ch. 8 - Prob. 23CT Ch. 8 - Prob. 24CT Ch. 8 - Prob. 25CT Ch. 8 - Prob. 26CT

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the 9 t h term of the geometric sequence using the table feature of a graphing utility.

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To find: the 9th<m:math><m:mrow><m:msup><m:mn>9</m:mn><m:mrow><m:mi>t</m:mi><m:mi>h</m:mi></m:mrow></m:msup></m:mrow></m:math> term of the geometric sequence using the table feature of a graphing utility.

Answer to Problem 34E

Explanation of Solution

To find: the 9th<m:math><m:mrow><m:msup><m:mn>9</m:mn><m:mrow><m:mi>t</m:mi><m:mi>h</m:mi></m:mrow></m:msup></m:mrow></m:math> term of the geometric sequence algebraically.

Answer to Problem 34E

Explanation of Solution

Chapter 8 Solutions

To find: the $9th$ term of the geometric sequence using the table feature of a graphing utility.

To find: the $9th$ term of the geometric sequence algebraically.