Question

Find the first 5 terms of the sequence defined by the formula
\[
u_{n}=5 n-4 .
\]

Answer 1

\[
\begin{aligned}
&u_{1}=5 \times 1-4=1 \\
&u_{2}=5 \times 2-4=6 \\
&u_{3}=5 \times 3-4=11 \\
&u_{4}=5 \times 4-4=16 \\
&u_{5}=5 \times 5-4=21
\end{aligned}
\]
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.