What is the pattern for the number of squares in each stage, and what is the formula for stage n?

Here's a breakdown of the pattern and the answers to your questions.

First, let's analyze the pattern to determine the number of squares at each stage:

• Stage 1: 4 squares
• Stage 2: 7 squares
• Stage 3: 10 squares

We can see that the number of squares increases by 3 for each subsequent stage ($7-4=3$, $10-7=3$). This is an arithmetic progression with a common difference of $d=3$.
The formula for the number of squares ($S_n$) at Stage $n$ can be found using the formula $S_n = S_1 + (n-1)d$.
Substituting $S_1=4$ and $d