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Chapter 14: Problem 72

What is an arithmetic sequence? Give an example with your explanation.

Short Answer

Expert verified
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. An example is the sequence 2, 4, 6, 8... where the first term is 2 and the common difference is 2.

Step by step solution

01

Understanding the Concept

An arithmetic sequence, also known as an arithmetic progression, is a sequence of numbers in which the difference between consecutive terms is constant. This difference can be either positive, negative or even zero.
02

Formulating the Definition Mathematically

This can be mathematically represented as such, where the \(n\)th term \(a_n\) of an arithmetic sequence can be written in the form: \(\ a_n = a_1 + (n-1) \cdot d \), where \(a_1\) is the first term in the sequence, \(n\) is the position of the term in the sequence, and \(d\) is the common difference.
03

Providing an Example

For instance, consider the sequence 2, 4, 6, 8... This is an arithmetic sequence because the difference between consecutive terms is constant, in this case, it is 2. The same sequence could be expressed as: \(a_n = 2+ (n-1) \cdot 2\), where 2 is the first term \(a_1\) and 2 is also the common difference, \(d\).

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Most popular questions from this chapter

Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. Evaluate without using a calculator: \(\frac{600 !}{599 !}\)

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Use the formula for the value of an annuity to solve Exercises. Round answers to the nearest dollar. To offer scholarship funds to children of employees, a company invests \(\$ 15,000\) at the end of every three months in an annuity that pays \(9 \%\) compounded quarterly. a. How much will the company have in scholarship funds at the end of ten years? b. Find the interest.

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Will help you prepare for the material covered in the next section. Use the formula \(a_{n}=4+(n-1)(-7)\) to find the eighth term of the sequence \(4,-3,-10, \ldots\)
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