Common difference

Definition

The common difference is the constant amount added or subtracted between consecutive terms in an arithmetic sequence. It is denoted by $d$.

5 Must Know Facts For Your Next Test

1. The formula for the $n$-th term of an arithmetic sequence is $a_n = a_1 + (n-1)d$, where $a_1$ is the first term and $d$ is the common difference.
2. If the common difference is positive, the sequence increases; if negative, it decreases.
3. The sum of the first $n$ terms of an arithmetic series can be calculated using $S_n = \frac{n}{2} (2a_1 + (n-1)d)$.
4. In any arithmetic sequence, each term can be expressed as a linear function of its position number.
5. The common difference can be found by subtracting any term from its successive term: $d = a_{n+1} - a_n$.

Review Questions

• What is the common difference in the arithmetic sequence 3, 7, 11, 15?
• How do you find the $10$-th term in an arithmetic sequence with a first term of 5 and a common difference of 3?
• What formula would you use to find the sum of the first 20 terms of an arithmetic series?

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 the previous term.

Series:

The sum of terms in a sequence.

$a_n$: Represents the n-th term in a sequence.