What is an Arithmetic Sequence?

Arithmetic Sequence: An arithmetic sequence is an ordered list of numbers in which the difference between any two consecutive terms is constant. This constant is called the common difference, denoted $d$ .

In an arithmetic sequence $u_{1}, u_{2}, u_{3}, \dots$ , each term is obtained by adding $d$ to the previous one:

$u_{n} = u_{n - 1} + d$

The common difference can be positive (increasing sequence), negative (decreasing sequence), or even zero (constant sequence).

Exam Tip

To find $d$ quickly, subtract any term from the one that follows it:
$d = u_{n + 1} - u_{n}$
This works for any consecutive pair in the sequence.

Note

You may see terms written as $a_{n}$ or $u_{n}$ , both notations mean exactly the same thing. IB exam papers typically use $u_{n}$ , so get comfortable with that.

Example

Consider the sequence: 3, 7, 11, 15, 19, …

First term: $u_{1} = 3$
Common difference: $d = 7 - 3 = 4$
Check: $11 - 7 = 4$ ✓, $15 - 11 = 4$ ✓

Each term is exactly 4 more than the previous one.

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What is an Arithmetic Sequence?

In an arithmetic sequence $u_{1}, u_{2}, u_{3}, \dots$ , each term is obtained by adding $d$ to the previous one:

$u_{n} = u_{n - 1} + d$

The common difference can be positive (increasing sequence), negative (decreasing sequence), or even zero (constant sequence).

Exam Tip

To find $d$ quickly, subtract any term from the one that follows it:
$d = u_{n + 1} - u_{n}$
This works for any consecutive pair in the sequence.

Note

You may see terms written as $a_{n}$ or $u_{n}$ , both notations mean exactly the same thing. IB exam papers typically use $u_{n}$ , so get comfortable with that.

Example

Consider the sequence: 3, 7, 11, 15, 19, …

First term: $u_{1} = 3$
Common difference: $d = 7 - 3 = 4$
Check: $11 - 7 = 4$ ✓, $15 - 11 = 4$ ✓

Each term is exactly 4 more than the previous one.

Free preview

SL 1.2—Sequences and Sigma Notation

What is an Arithmetic Sequence?

7 more sections in this topic

SL 1.2—Sequences and Sigma Notation

What is an Arithmetic Sequence?

7 more sections in this topic