Which figure in the pattern below will have 99 squares?
Figure 1
(picture of 1 square)
Figure 2
(picture of 3 squares)
Figure 3
(picture of 5 squares)
10
To determine which figure in the pattern will have 99 squares, we can observe the pattern to find a relationship between the figure number and the number of squares.
In this given pattern, it appears that the number of squares in each figure is increasing by 2 with each consecutive figure. Figure 1 has 1 square, Figure 2 has 3 squares (1 + 2), and Figure 3 has 5 squares (3 + 2).
We can establish a general expression to calculate the number of squares in any given figure:
Number of squares = 1 + (figure number - 1) * 2
Using this expression, we can find the figure that will have 99 squares by equating the expression to 99 and solving for the figure number:
99 = 1 + (figure number - 1) * 2
To solve for figure number, let's rearrange the equation:
98 = (figure number - 1) * 2
Divide both sides by 2:
49 = figure number - 1
Add 1 to both sides:
50 = figure number
Therefore, Figure 50 will have 99 squares according to this pattern.