Look for a part repeated once per position and any fixed extra part. In a row of joined squares, the first square uses four sticks. Each new square shares a side and needs only three new sticks. Example T_n=4+3(n-1) =3n+1 A row of 12 squares needs 3(12)+1=37 sticks. Counting four sticks per square would count shared sides twice. The same expression can be seen as n top sticks, n bottom sticks and n+1 vertical sticks. Both counts give 3n+1.

Look for a part repeated once per position and any fixed extra part. In a row of joined squares, the first square uses four sticks. Each new square shares a side and needs only three new sticks.

\(\begin{aligned}T_n&=4+3(n-1)\\&=3n+1\end{aligned}\)

A row of \(12\) squares needs \(3(12)+1=37\) sticks. Counting four sticks per square would count shared sides twice.

The same expression can be seen as \(n\) top sticks, \(n\) bottom sticks and \(n+1\) vertical sticks. Both counts give \(3n+1\).

Counting a growing pattern

Counting a growing pattern