What is the general term formula for an arithmetic sequence?

The formula for the general term of an arithmetic sequence is indeed expressed as ( a_n = a_1 + d(n-1) ). In this formula, ( a_n ) represents the ( n )-th term of the sequence, ( a_1 ) is the first term, ( d ) is the common difference between consecutive terms, and ( n ) is the term number.

An arithmetic sequence is defined as a sequence of numbers in which the difference between any two consecutive terms is constant. This is where the common difference ( d ) comes into play. By taking the first term ( a_1 ) and adding the common difference ( d ) multiplied by one less than the term number ( n ), we can effectively generate any term in the sequence.

For example, if you start with a first term of 3 and have a common difference of 2, the sequence would look like 3, 5, 7, 9, and so on. According to the formula, the 5th term (where ( n = 5 )) would be calculated as ( a_5 = 3 + 2(5-1) = 3 + 8 =