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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

4 9 - 5 4 Chapter 13.CR, Problem 51E, 49-54 Sums of Arithmetic and Geometric Sequences Determine whether the expression is a partial sum Sums of Arithmetic and Geometric Sequences Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum.

5 + 2 5 + 3 5 + + 100 5

To determine

Whether the expression 5+25+35++1005 is partial sum of arithmetic or geometric sequence. Then find the sum.

Explanation

Given:

The expression is given as,

5+25+35++1005

Approach:

Check if the terms in the expression have a common difference or a common ratio.

Calculation:

Find the common difference.

255=53525=5

So there is a common difference of 5.

This proves that the given expression is a partial sum of an arithmetic sequence with first term a=5, common difference, d=5

The nth term in this arithmetic sequence is a+(n1)d=5+(n1)5

We set this equal to 1005 to compute number of terms in the expression.

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Chapter 13 Solutions

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