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Chapter 9: Problem 24

Find a formula for \(a_{n}\) for the arithmetic sequence. $$a_{1}=100, d=-8$$

Short Answer

Expert verified
The formula for the arithmetic sequence is \(a_{n} = 108 - 8n\).

Step by step solution

01

Identify the given terms

From the given exercise, the first term \(a_{1}\) is 100 and the common difference \(d\) is -8.
02

Substitute the given values into the formula

Substitute \(a_{1} = 100\) and \(d = -8\) into the arithmetic sequence formula, which gives the general formula as \(a_{n} = 100 + (n-1) \cdot -8\).
03

Simplify the formula

This will give the simplified formula as \(a_{n} = 100 - 8 \cdot (n-1)\), which can be simplified further to \(a_{n} = 108 - 8n\).

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