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.

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Question

Chapter 8, Problem 37RE

To determine

To write formula for $nth$ term $an$ and sum of the first $25$ terms of the Arithmetic sequence -

$a1=100$ ; $d=−3$

Expert Solution & Answer

Answer to Problem 37RE

Theformula for $nth$ term is $an=103−3n$ and sum of the first $25$ terms is $1600$ .

Explanation of Solution

Given: ArithmeticSequence: $a1=100$ ; $d=−3$

Formula Used:

$nth$ term for an ArithmeticSequence is $tn=a+(n−1)d$

Sum of an Arithmetic Sequence: $Sn=n2[2a+(n−1)d]$

Calculation:

Given: ArithmeticSequence: $a1=100$ ; $d=−3$

Using above formula, we have:

$tn=a+(n−1)d$

$an=100+(n−1)(−3)an=100−3n+3an=103−3n$

Thus, the formula for $nth$ term is $an=103−3n$ .

Sum of an Arithmetic Sequence: $Sn=n2[2a+(n−1)d]$

$S25=252[2(100)+(25−1)(−3)]S25=252[200+24(−3)]S25=252(200−72)S25=252×128S25=1600$

The sum is $1600$ .

Conclusion:

Hence, the formula for $nth$ term is $an=103−3n$ and sum of the first $25$ terms is $1600$ .

Chapter 8, Problem 36RE

Chapter 8, Problem 38RE

Chapter 8 Solutions

Precalculus with Limits: A Graphing Approach

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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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To write formula for n t h term a n and sum of the first 25 terms of the Arithmetic sequence - a 1 = 100 ; d = − 3

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