A. Pentagonal Numbers are numbers that create a pentagon. In other words: 1, 5, 12, 22, etc.
B. The nth pentagonal number can be found by the formula:
n(3n - 1)
C. In number sense, the question will only ask for the nth pentagonal number.
Ex  The 8th pentagonal number is __________.
a. Using the formula we get: (8)(23)/2 or 4 x 23 = 92.
b. The answer is 92.
Ex  The 13th pentagonal number is __________.
a. Using the formula we get: (13)(38)/2 or 13 x 19 = 247.
b. The answer is 247.
D. Here are some ways of manipulating pentagonal numbers:
1. The difference of successive pentagonal numbers is:
3n - 2, where n is the largest
2. Adding successive pentagonal numbers gives:
3n2 - 4n + 2, where n is the largest
NOTE: You might see #1 on a test, but I doubt you will ever see #2 on a test.