Question

Find the general term of the sequence
\[
1,4,9,16,25, \ldots
\]

Answer 1

\[
\begin{aligned}
&1,4,9,16,25, \ldots \\
&u_{1}=1=1 \times 1 \\
&u_{2}=4=2 \times 2 \\
&u_{3}=9=3 \times 3 \\
&u_{4}=16=4 \times 4 \\
&u_{5}=25=5 \times 5
\end{aligned}
\]
This sequence can be described by the general formula
\[
u_{n}=n^{2} .
\]