the sequence of figures shows a pattern. if the pattern repeats, how many small squares will figure 4 have?

Explanation:

Step1: Analyze the number of squares in each figure

Figure 1 has 1 square. Figure 2 has 1 + 6=7 squares. Figure 3 has 1+6 + 6=13 squares.

Step2: Identify the pattern

The number of additional squares in each successive figure is 6. The formula for the number of squares in the $n$th figure can be written as $a_n=a_1+(n - 1)d$, where $a_1 = 1$ (the number of squares in Figure 1), $d = 6$ (the common - difference), and $n$ is the figure number.

Step3: Calculate for Figure 4

For $n = 4$, we substitute into the formula $a_n=1+(n - 1)\times6$. So $a_4=1+(4 - 1)\times6=1 + 18=19$.

Answer:

19