\[

\begin{aligned}

&u_{1}=5 \times 1-4=1 \\

&u_{2}=5 \times 2-4=6 \\

&u_{3}=5 \times 3-4=11 \\

&u_{4}=5 \times 4-4=16 \\

&u_{5}=5 \times 5-4=21

\end{aligned}

\]

So the sequence is

\[

1,6,11,16,21, \ldots

\]

Here the terms increase by 5 each time and the formula contains a ' \(5 n\) '.

In general, if the terms of a sequence increase by a constant amount, \(d\), each time, then the sequence will be defined by the formula

\[

u_{n}=d n+c

\]

where \(c\) is a constant number.