Number Patterns Consider the pattern of dots shown below.
a. Find the next figure in this pattern.
b. Write a sequence to represent the number of dots added to the previous figure to create the next figure in this pattern. The first term in your sequence should be 1.
c. Find the general form for the nth term of the sequence found in part b.
d. Determine a formula that will calculate the total number of dots for the nth figure in this dot pattern.
e. Prove that the formula found in part d is correct using mathematical induction.