HOME
Miscellaneous Elementary Junior High Sum Of Positive Integral Divisors High School Manipulating Polygonal Numbers

Pentagonal Numbers:A. Pentagonal Numbers are numbers that create a pentagon. In other words: 1, 5, 12, 22, etc. B. The n^{th} pentagonal number can be found by the formula: n(3n  1) 2 C. In number sense, the question will only ask for the n^{th} pentagonal number. Ex [1] The 8^{th} pentagonal number is __________. a. Using the formula we get: ^{(8)(23)}/_{2} or 4 x 23 = 92. b. The answer is 92. Ex [2] The 13^{th} 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: 3n^{2}  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.
