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- The sequence of square numbers, 1, 4, 9, 1 6, 2 5, … , is made up of squares of integers. A square is a number multiplied by itself. 1 ⋅ 1 = 1, The first number of the sequence is the square of 1, which is 1 2 = 1. 2 ⋅ 2 = 4, the second number if the sequence is the square of 2, which is 2 2 = 4.
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Surprising Patterns in the Square Numbers (1, 4, 9, 16…) A quick puzzle for you — look at the first few square numbers: 1, 4, 9, 16, 25, 36, 49…. And now find the difference between consecutive squares: 1 to 4 = 3. 4 to 9 = 5. 9 to 16 = 7. 16 to 25 = 9. 25 to 36 = 11.
- Arithmetic Sequences. An Arithmetic Sequence is made by adding the same value each time. Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ... This sequence has a difference of 3 between each number.
- Geometric Sequences. A Geometric Sequence is made by multiplying by the same value each time. Example: 1, 3, 9, 27, 81,243, ... This sequence has a factor of 3 between each number.
- Special Sequences. There are also many special sequences, here are some of the most common
- Triangular Numbers. 1, 3, 6, 10, 15, 21, 28, 36, 45, ... This Triangular Number Sequence is generated from a pattern of dots that form a triangle. By adding another row of dots and counting all the dots we can find the next number of the sequence
A square number is a number multiplied by itself. This can also be called 'a number squared'. The symbol for squared is ². 2² = 2 x 2 = 4. 3² = 3 x 3 = 9. 4² = 4 x 4 = 16. 5² = 5 x 5 = 25
Square and cube numbers are special sequences of numbers that are linked to the property of the shape they are named after. A square number relates to the area of a...
There are some special sequences that you should be able to recognise. The most important of these are: Square numbers: 1, 4, 9, 16, 25, 36, … - the nth term is \ (n^2\). Cube...
The sequence of square numbers, 1, 4, 9, 1 6, 2 5, … , is made up of squares of integers. A square is a number multiplied by itself. 1 ⋅ 1 = 1, The first number of the sequence is the square of 1, which is 1 2 = 1. 2 ⋅ 2 = 4, the second number if the sequence is the square of 2, which is 2 2 = 4.
Square Sequences. A #Square Number# is the result of multiplying an integer by itself. For example, 4 x 4 = 16. The first 5 square numbers are shown below in a diagram form: A shorthand way of writing a square number is to use an #index#: 4 x 4 = 4 2. Square numbers can be written as a sequence: Example 1. What is the next square number after 81?
