Number Patterns

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Numbers form beautiful patterns in relation to other numbers. Students can be given the first few statements in a pattern. Using logic, they can write a few more steps. They can also verify the truth of these statements by actual calculations.

Here are a few patterns. The Internet can yield many more such patterns.

1 x 8 + 1 = 9           12 x 8 + 2 = 98            123 x 8 + 3 = 987            1234 x 8 + 4 = 9876            12345 x 8 + 5 = 98765            123456 x 8 + 6 = 987654            1234567 x 8 + 7 = 9876543            12345678 x 8 + 8 = 98765432            123456789 x 8 + 9 = 987654321             1 x 9 + 2 = 11            12 x 9 + 3 = 111            123 x 9 + 4 = 1111            1234 x 9 + 5 = 11111            12345 x 9 + 6 = 111111            123456 x 9 + 7 = 1111111            1234567 x 9 + 8 = 11111111            12345678 x 9 + 9 = 111111111            123456789 x 9 +10= 1111111111             9 x 9 + 7 = 88            98 x 9 + 6 = 888            987 x 9 + 5 = 8888            9876 x 9 + 4 = 88888            98765 x 9 + 3 = 888888            987654 x 9 + 2 = 8888888            9876543 x 9 + 1 = 88888888            98765432 x 9 + 0 = 888888888               1 x 1 = 1            11 x 11 = 121            111 x 111 = 12321            1111 x 1111 = 1234321            11111 x 11111 = 123454321            111111 x 111111 = 12345654321            1111111 x 1111111 = 1234567654321            11111111 x 11111111 = 123456787654321            111111111 x 111111111=12345678987654321

Sum of any sequence of odd numbers, starting with 1 will always be a square.

The square of the sum of some numbers starting with 1 will be equal to the cubes of the individual numbers,

(1 + 2 + 3 + 4 )2 = 13 + 23 + 33 + 43

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