Question

Write series with summation notation. $5+1+(-3)+(-7)$

   Write series with summation notation.
$5+1+(-3)+(-7)$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 11, Problem 24

Instant Answer

Solved by Expert Edward Downes

07/16/2020

Step 1

In this case, the series is arithmetic because it has a common difference. The common difference is -4 (1-5 = -4, -3-1 = -4, -7-(-3) = -4). Show more…

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Write series with summation notation. $5+1+(-3)+(-7)$

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Key Concepts

Summation Notation

Summation notation is a method to represent the sum of a sequence of terms compactly using the sigma symbol (?). It includes an index of summation that iterates over a specified range and a general formula for the nth term. In this context, the series can be rewritten by identifying the first term and constant difference to form a general term, and then summing over the required range.

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In the given series, each term decreases by 4 from the previous term, indicating a common difference of -4, which is a defining feature of an arithmetic sequence.

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