Arithmetic Sequences
An Arithmetic Sequence is made by adding some value each time.
1, 4, 7, 10, 13, 16, 19, 22, 25, ... |
3, 8, 13, 18, 23, 28, 33, 38, ... |
The value added each time is called the "common difference"
What is the common difference in this example?
19, 27, 35, 43, ... |
The common difference could also be negative, like this:
25, 23, 21, 19, 17, 15, ... |
A Geometric Sequence is made by multiplying by some value each time.
2, 4, 8, 16, 32, 64, 128, 256, ... |
3, 9, 27, 81, 243, 729, 2187, ... |
1, 3, 6, 10, 15, 21, 28, 36, 45, ... |
This sequence is generated from a pattern of dots which form a triangle.
By adding another row of dots and counting all the dots we can find the next number of the sequence:
1, 4, 9, 16, 25, 36, 49, 64, 81, ... |
The next number is made by squaring where it is in the pattern.
The second number is 2 squared (22 or 2×2)
The seventh number is 7 squared (72 or 7×7) etc
1, 8, 27, 64, 125, 216, 343, 512, 729, ...
The next number is made by cubing where it is in the pattern.
The second number is 2 cubed (23 or 2×2×2)
The seventh number is 7 cubed (73 or 7×7×7) etc
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... |
The next number is found by adding the two numbers before it together.
The 2 is found by adding the two numbers in front of it (1+1)
The 21 is found by adding the two numbers in front of it (8+13)
The next number in the sequence above would be 55 (21+34)
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