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Chapter 9: Problem 26

Find a formula for \(a_{n}\) for the arithmetic sequence. $$4, \frac{3}{2},-1,-\frac{7}{2}, . .$$

Short Answer

Expert verified
The formula for the nth term of the sequence is \(a_{n} = 4 + (n - 1)(-\frac{5}{2})\).

Step by step solution

01

Find the Common Difference

To find the common difference of this sequence, subtract the second term from the first term. \[d = \frac{3}{2} - 4 = -\frac{5}{2}\]
02

Use the General Form of an Arithmetic Sequence

The general form of an arithmetic sequence is \(a_{n} = a_{1} + (n-1)d\), where \(a_{n}\) is the nth term, \(a_{1}\) is the first term, \(n\) is the term number, and \(d\) is the common difference. In this instance, \(a_{1} = 4\) and \(d = -\frac{5}{2}\).
03

Substitute the Values

By substituting the values into the formula, the general term for the given sequence is calculated. \[a_{n} = 4 + (n - 1)(-\frac{5}{2})\]

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Most popular questions from this chapter

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