Found some old notes that may be of help when revising.......
Arithmetic Sequences
An Arithmetic Sequence is made by adding some value each time.
Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ... This sequence has a difference of 3 between each number. The pattern is continued by adding 3 to the last number each time.
Example: 3, 8, 13, 18, 23, 28, 33, 38, ... This sequence has a difference of 5 between each number. The pattern is continued by adding 5 to the last number each time. The value added each time is called the "common difference" What is the common difference in this example? 19, 27, 35, 43, ...
Answer: The common difference is 8 The common difference could also be negative, like this: 25, 23, 21, 19, 17, 15, ... This common difference is 2 The pattern is continued by subtracting 2 each time.
Geometric Sequences A Geometric Sequence is made by multiplying by some value each time.
Example: 2, 4, 8, 16, 32, 64, 128, 256, ... This sequence has a factor of 2 between each number. The pattern is continued by multiplying by 2 each time.
Example: 3, 9, 27, 81, 243, 729, 2187, ... This sequence has a factor of 3 between each number. The pattern is continued by multiplying by 3 each time.
Special Sequences
Triangular Numbers 1, 3, 6, 10, 15, 21, 28, 36, 45, ... This Triangular Number 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: Square Numbers 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
Cube Numbers 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
Fibonacci Numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The Fibonacci Sequence is found by adding the two numbers before it together. The 2 is found by adding the two numbers before it (1+1) The 21 is found by adding the two numbers before it (8+13) The next number in the sequence above would be 55 (21+34)
