a. 

This problem also shows the first three figures of a growing pattern. This problem not only requires students to find the number of dots needed to make the 6th figure in the pattern, however; it also requires students to determine whether it is possible for one of the terms to use 84 dots.

b. 

This problem uses a growing pattern, and the nth term uses 2 more dots than the previous term.

c. 

This problem can be used to help students learn to write a general rule for the nth term of a function.

d. 

This problem asks students to find the number of dots needed for the 100th term, but could be further extended to ask for the number of dots needed for the nth term. Again ask students to describe how to build each term. Look for answers that relate each figure to its place in the pattern. For example, students might notice that the 1st term uses 1 dot + 1 pair of dots, the 2nd term uses 1 dot + 2 pairs of dots, the 3rd term uses 1 dot + 3 pairs of dots, and so forth. The nth term uses 1 dot + n pairs of dots, for a total of 2n + 1 dots.