Problem 74 - College Algebra

Question

Explain how to find the general term of an arithmetic sequence.

Step-by-Step Solution

Answer

The general term of an arithmetic sequence could be found using the formula \(a_n = a_1 + (n-1)*d\), where \(a_n\) is the nth term, \(a_1\) is the first term, \(n\) is the number of terms and \(d\) is the common difference of the sequence.

Step 1: Identify first term and common difference

Initially identify the first term (denoted by \(a_1\)). Afterwards, identify the common difference (denoted by \(d\)) from the arithmetic sequence. The common difference could be gained by subtracting the first term from the second term, or the nth term from the \(n+1\)th term.

Step 2: Formulate the general term formula

Following that, the general formula for an arithmetic sequence which is \(a_n = a_1 + (n-1)*d\), where \(a_n\) is the nth term, \(n\) is the number of terms, and \(d\) is the common difference, would be used. With this formula, any term in the sequence can be found.

Step 3: Plug the specific values into the formula

Lastly, insert the specific values of the initial term \(a_1\) and the common difference \(d\) that we found in Step 1 into the general formula.