Arithmetic Sequences - nth Term

What is an Arithmetic Sequence?
An arithmetic sequence (also called an arithmetic progression) is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference.

What is the formula for the nth term of an arithmetic sequence?
An arithmetic sequence is defined by its first term and the common difference. The formula for the nth term of an arithmetic sequence is:
a_n = a₁ + (n-1)d, where a₁ is the first term, d is the common difference and a_n is the nth term of the sequence.

The following diagrams give an arithmetic sequence and the formula to find the n^th term. Scroll down the page for more examples and solutions.

Sequence Worksheets
Practice your skills with the following sequence worksheets:
Printable & Online Sequence Worksheets

Arithmetic Sequences
This video covers identifying arithmetic sequences and finding the nth term of a sequence. It includes four examples.

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Arithmetic Sequences: A Formula for the n^th Term.
This video shows how to derive the formula to find the n^th term of a sequence by considering an example. The formula is then used to solve some problems.

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In this video we look at two different ways of finding the general term of an arithmetic sequence.

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This video focuses on Arithmetic Sequences
Determining the nth Term.

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Properties of an Arithmetic Sequence

1. Linear Growth: The sequence increases or decreases by a constant amount (d) each time.
2. Common Difference: The difference between consecutive terms is always the same.
3. Graph Representation: When plotted on a graph, the terms of an arithmetic sequence lie on a straight line.

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