Chapter 8.2, Problem 28PPS

To determine

Based on the figure below, which figures will have 40 squares.

  

Answer to Problem 28PPS

The 13^th figure will have 40 squares.

Explanation of Solution

Given information:

  

Calculation:

Number of beams(n)	1	2	3
Number of squares(t)	4	7	10

The difference of the number of beams is 1, and that of the number of square is 3

The pattern in the table shows the equation $t=3n+1$

Using the equation, we will determine, which figure will have 40 squares, t= 40

  $\begin{array}{l}40=3n+1\\ \Rightarrow 40-1=3n+1-1\\ \Rightarrow 39=3n\\ \Rightarrow \frac{39}{3}=\frac{3n}{3}\\ \Rightarrow n=13\end{array}$