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Chapter 9: Problem 28

Find a formula for \(a_{n}\) for the arithmetic sequence. $$a_{1}=-4, a_{5}=16$$

Short Answer

Expert verified
The formula for the \(n\)th term of the arithmetic sequence is \(a_{n} = 5n - 9\).

Step by step solution

01

Find the common difference

The common difference \(d\) can be found using the formula \(d = \frac{a_{n} - a_{1}}{n - 1}\). Here, \(a_{5} = 16\), \(a_{1} = -4\), and \(n = 5\). So, \(d = \frac{16 - (-4)}{5 - 1} = \frac{20}{4} = 5\).
02

Find the formula for \(a_{n}\)

Now that we have the common difference \(d = 5\), we can plug it into the formula for the \(n\)th term of an arithmetic sequence. Hence, \(a_{n} = -4 + (n - 1) * 5\). After simplifying, we obtain \(a_{n} = 5n - 9\).

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