Problem 73 - College Algebra

Question

What is the common difference in an arithmetic sequence?

Step-by-Step Solution

Answer

The common difference in an arithmetic sequence is the constant value between any two consecutive terms in the sequence and can be found by the formula \( d = a_n - a_{n-1} \) , where \( d \) is the common difference, \( a_n \) is any term in the sequence and \( a_{n-1} \) is the term before \( a_n \) .

Step 1: Understanding the concept of an Arithmetic sequence

An arithmetic sequence refers to a sequence of numbers in which the difference of any two successive members is a constant. This difference is referred to as the common difference.

Step 2: Formula for Common Difference

The formula for the common difference \( d \) in an arithmetic sequence is \( d = a_n - a_{n-1} \) , where \( a_n \) is the nth term of the sequence and \( a_{n-1} \) is the term before \( a_n \).

Step 3: Identifying the common difference

To find the common difference, subtract any term in the sequence from the term that follows it. The result is the common difference of the arithmetical sequence.