Number Sequences – Examples and Types


 

Arithmetic Sequences

An Arithmetic Sequence is made by adding some value each time. Examples:

  • 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.
  • 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”. 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. Examples:

  • 2, 4, 8, 16, 32, 64, 128, 256, … This sequence has a factor of 2 between each number. The pattern is continued by multiplying the last number by 2 each time.
  • 3, 9, 27, 81, 243, 729, 2187, … This sequence has a factor of 3 between each number. The pattern is continued by multiplying the last number by 3 each time.


 

Special Number Sequences

 

Triangular Numbers

  • 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.

 

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 (2×2). The seventh number is 7 squared (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 (2×2×2) The seventh number is 7 cubed (7×7×7) etc..

 

Fibonacci Numbers

  • 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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