Chapter 1.1, Problem 10PPSE

Solution

To draw the next likely figure in each pattern.

The first pattern has one circle, the second pattern has three circles, the third pattern has six circles and the fourth pattern has ten circles. The fifth pattern will have fifteen circles.

Given information:

To describe each pattern using words and to draw the next likely figure in each pattern.

  

Explanation:

The first pattern has one circle, the second pattern has three circles, the third pattern has six circles and the fourth pattern has ten circles.

From first pattern to the second pattern, the number of circles increased by two. From second pattern to the third pattern, the number of circles increased by three and from third pattern to the fourth pattern, the number of circles increased by four.

From the pattern, the number of circles increased from fourth to fifth pattern will be one more than the increased number of circles from the third to fourth pattern:

So, the number of circles in the fifth pattern will be five more than the number of circles in the fourth pattern:

Number of circles in the fourth pattern is $10$ :

Number of circles in the fifth pattern will be $10+5=15$ as shown below: