Arithmetic Sequences
Find and use arithmetic sequences with a constant difference.
An arithmetic sequence increases or decreases by adding the same number each time. This number is the common difference, written \(d\).
Nth term formula\[u_n=u_1+(n-1)d\]
Worked example
The sequence \(7, 11, 15, 19, \ldots\) has \(u_1=7\) and \(d=4\).
\[u_n=7+(n-1)4=4n+3\]So the 20th term is \(u_{20}=4(20)+3=83\).
Exam tip
If you are given two terms, subtract their formulas. For example, if \(u_5=18\) and \(u_{12}=46\), then \(7d=28\), so \(d=4\).