Problem 73 - Algebra and Trigonometry

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 obtained when we subtract any term in the sequence (except the first one) from its immediately preceding term.

Step 1: Understanding Arithmetic Sequence

In mathematics, an arithmetic sequence, also known as an arithmetic progression, is a sequence of numbers in which the difference of any two successive members is a constant. This means each term in the sequence after the first is created by adding a certain value to the previous term.

Step 2: Identifying the Common Difference

The constant difference that you get after subtracting any term in the sequence (except the first one) from its immediately preceding term is called the 'common difference'. It can be positive, negative, or zero.

Step 3: Calculation of Common Difference

To calculate the common difference in an arithmetic sequence, subtract the first term from the second term. Alternately, you can subtract any term in the sequence from the term that immediately follows it. The result is the common difference. Symbolically, if an arithmetic sequence has terms denoted as \( a_1, a_2, a_3, a_4, \ldots, a_n \), then common difference 'd' can be calculated as \( d = a_2 - a_1 \) or \( d = a_{n+1} - a_n \).