Arithmetic sequences

Use the common difference to find terms and sums and interpret change.

Meaning

An arithmetic sequence has a constant difference between consecutive terms. With first term and common difference the th term is

Example

A sequence with first term 5 and common difference 3 begins 5, 8, 11, 14, …. Its sixth term is There are changes from the first term to the th, not The common difference can be negative or zero.

Practice for this concept

Scope and references

Topics

Common difference, general term, arithmetic mean, sums

Learning goal

Use the common difference to find terms and sums and interpret change.

Helpful background

Connect term indices with a constant difference.

Arithmetic-sequence rules

Does not include sums of arithmetic sequences or arithmetic means between terms.

Explore a concept