Visual Algebra

The expression has a $1$ for the $1$ constant square starting on step $0,$ and a $3n$ for the $3$ squares added at each step. The total is $3n+1.$

The letter $n$ represents the step number.

How many squares are in step $n$ of the pattern?

The expression has a $4$ for the $4$ constant squares starting on step $0,$ and an $n$ for the $1$ square added at each step.

At each step, $5$ squares are added, so there are at least $5n$ squares in the $n$th step.

Backing up shows there are $2$ shapes on step $0,$ so a constant $2$ is also in the expression. The total is $5n+2.$