Miscellaneous

Elementary
GCD
LCM
Definitions

Percents

Ratios

Square Roots

Reverses

Junior High
Cube Roots

Mult By 9 (#1)
Mult By 9 (#2)

Mult By 8

Polynomials

Positive Integral Divisors

Sum Of Positive Integral Divisors

Relatively Prime 

Triangular Numbers

Remainders

Divide By 40

Divide By 25

Divide By 9

High School

Pentagonal Numbers

Hexagonal Numbers

Heptagonal Numbers

Octagonal Numbers

Manipulating Polygonal Numbers

Dividing Factorials #1

Dividing Factorials #2

Solving Triangular Numbers

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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:

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.

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