Question

Refer to the first three arrays of numbers below.

Make drawings to find the next three numbers in this pattern.

Short answer

The next three figures in the pattern are:

Step-by-step solution

Step 1. Given Information.

Given pattern is:

Step 2. Calculation.

From the pattern it is seen that the first figure is just a point.

The second pattern is a polygon with 5 points.

The third pattern is 2 polygons with a common point i.e. $5\times 2-1=10-1=9$ points.

So, the next pattern is 3 polygons with a common point, then 4 polygons with a common point and then 5 polygons with a common point.

Step 3. Conclusion.

Hence, the next three figures in the pattern are: