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Chapter 6: Problem 59

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(a_{n}=a_{1}+(n-1) d\) for \(n\)

Short Answer

Expert verified
The variable \(n\) in the equation \(a_{n}=a_{1}+(n-1) d\) can be solved to get \(n = ((a_{n} - a_{1})/d) + 1\)

Step by step solution

01

Understand the Equation

The original equation is \(a_{n}=a_{1}+(n-1) d\). This describes the nth term of an arithmetic sequence.
02

Rearrange the Equation

Start by isolating terms with \(n\) on one side of the equation. In order to isolate \(n\), subtract \(a_{1}\) from both sides to get \(a_{n} - a_{1} = (n-1)d\).
03

Solve for n

Now, divide both sides of the equation by \(d\) to solve for \(n\), this gives \((a_{n} - a_{1})/d = n-1\). Finally, add 1 to both sides of the equation to totally isolate \(n\), giving \(n = ((a_{n} - a_{1})/d) + 1\) as the final answer.

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