Common difference

Definition

The common difference is the constant amount that each term in an arithmetic sequence differs from the previous term. It is denoted by 'd' and can be positive, negative, or zero.

5 Must Know Facts For Your Next Test

1. The common difference $d$ can be found by subtracting any term from the subsequent term in an arithmetic sequence.
2. In the arithmetic sequence formula $a_n = a_1 + (n-1)d$, $d$ represents the common difference.
3. If $d > 0$, the sequence is increasing; if $d < 0$, the sequence is decreasing.
4. The sum of an arithmetic series can be calculated using $S_n = \frac{n}{2} (2a_1 + (n-1)d)$ where $S_n$ is the sum of the first n terms, $a_1$ is the first term, and $d$ is the common difference.
5. Common difference remains constant throughout an entire arithmetic sequence.

Review Questions

• How do you calculate the common difference in an arithmetic sequence?
• What does it mean for a sequence if its common difference is negative?
• Write out the formula for finding a specific term in an arithmetic sequence and identify where you use the common difference.

Related terms

Arithmetic Sequence: A sequence of numbers in which each term after the first is obtained by adding a constant (the common difference) to its predecessor.

Arithmetic Series: The sum of all terms in an arithmetic sequence up to a specified number of terms.

$a_n$: $a_n$ represents the nth term in an arithmetic sequence and can be found using $a_n = a_1 + (n-1)d$.