Page 93 - Knowledge Organiser Yr9 24-25

Knowledge Base: Mathematics Topic 25: Patterns and Sequences Year 9 | Autumn Term, 1st Half
By the end of this topic you should be able to:
• Find and use sequences and types of sequences
• Find and use term to term rule of sequences
• Find and use position to term rule of sequences
• Find and use geometric sequences
• Find and use sequences and patterns
• Find and use real life sequences
Language
Meaning
Example
Sequence
An ordered list of numbers, called terms, which often follow a pattern
2,5,8,11,... is a sequence
Position
A number that counts the terms, in order, starting from 1
The first term has position 1, the second term has position 2 etc.
Term-to-term rule
An instruction for how to get from one term in a sequence to the next term
For the sequence above the rule is +3
Position-to- term rule
A rule which works out the value of any term from its position in the sequence
For the sequence above, the term in the nth position is given by 3n-1
Geometric sequence
A sequence in which the term- to-term rule is multiplied by a fixed number
2, 6, 18, 54, 162, ...
Each term is 3× the previous term
Important things to remember:
1) Substitute a number for n to find the number term
2) Linear nth term is of the form an+b
3) Geometric sequence is of the form a×rn-1 , where a is the first term and r is the common ratio (multiplier)
Worked examples
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