Step-by-step explanation:
Here's how the number of dots increases as the figure number increases:
Figure 0: 1 dot (central dot)
Figure 1: 1 dot (central dot) + 6 dots (arranged in a hexagon around the central dot) = 7 dots
Figure 2: 7 dots (from Figure 1) + 12 dots (arranged in a larger hexagon around the previous hexagon) = 19 dots
Figure 3: 19 dots (from Figure 2) + 18 dots (arranged in a yet larger hexagon around the previous hexagon) = 37 dots
Following this pattern, we can determine the number of dots in any figure based on the figure number:
The number of dots in any figure is equal to the sum of 1 and the product of 6 times the figure number (n).
In other words, Dots in Figure n = 1 + 6n
Therefore, to find the number of dots in any figure, you just need to multiply the figure number (n) by 6 and add 1.
For Figures 0, 4, and 5, here's the calculation of the number of dots:
Dots in Figure 0: 1 + (6 * 0) = 1 dot
Dots in Figure 4: 1 + (6 * 4) = 25 dots
Dots in Figure 5: 1 + (6 * 5) = 31 dots
