Sequences Sequences are patterns. Each pattern or number in a sequence is called a term. The number at the start is called the first term. The term-to-term.

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Sequences Sequences are patterns. Each pattern or number in a sequence is called a term. The number at the start is called the first term. The term-to-term rule shows how you get the next term. For example, the first term in a sequence is 3 and the term-to-term rule is add 4 3, 7, 11, 15

Sequences where the numbers increase are called ascending sequences. For example 3, 6, 9,... A sequence, which carries on forever, is infinite. A sequence, which has only a fixed number of terms, is finite. A sequence can be made with decimal or negative numbers.

Square numbers form a square pattern of dots. Triangle numbers form a triangular pattern of dots. You can use the position-to-term rule to find any term in the sequence without having to write the whole sequence. An arithmetic sequence goes up or down in equal sized steps. For example, 2, 5, 8, 11, 14,... goes up in steps of 3.

Triangular numbers: Number of diagonals of a convex 2-D-shape with m vertexes: Some Quadratic sequences:

Function machines You can find the output of a function machine if you know the input. You can find the input of a function machine by using inverse operations. You can find the function if you have inputs and outputs.

Expressions and Mappings To help you remember the order of operations, use BIDMAS: Brackets, Indexes (powers), Division and Multiplication then Addition and Subtraction. In an algebraic expression, letters stand for mystery numbers. You can simplify expressions by collecting like terms. Like terms have the same letter, or no letter. You can use arithmetic operations with algebra. For example, 2 x 4p = 2 x 4 x p = 8p. Mappings are another way of writing function machine. A mapping can be shown on a mapping diagram.

Constructing Expressions You write an algebraic expression by using letters to stand for the numbers. For example, if a mystery number is p, you can write three times this number as 3p. The letter standing for a number is called a variable because its value can change or vary. In the example, p is the variable.

Decimals Digits after the decimal point are fractions: 0.1 (one tenth), 0.01 (one hundredth), (one thousandth), and so on. To compare decimal measurements, all the measurements must be in the same units. When you multiply a number by 10, the digits move one place to the left. When you divide a number by 10, the digits move one place to the right. To order decimals, first compare the whole numbers, next compare the tenths, then compare the hundredths, and so on.