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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Octagonal Numbers:

A.  An Octagonal Number is a number that creates a octagon.  In other words:  1, 8, 21, 40, etc.

B.  The n^th octagonal number can be found by the following:

n(3n - 2)

C.  In number sense, the question will only ask for the n^th octagonal number.

Ex [1]  The 8^th octagonal number is __________.

a.  Using the formula we get: 8 x 22 = 176.

b. The answer is 176.

Ex [2]  The 11^th octagonal number is __________.

a.  Using the formula we get: 11 x 31  = 343.

b.  The answer is 343.

D.  Here are some ways of manipulating octagonal numbers:

1.  The difference of successive octagonal numbers is:

6n - 5, where n is the largest

2.  Adding successive octagonal numbers gives:

6n² - 10n + 5, 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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