Sequences — Year 7 Revision Notes
These notes cover continuing sequences, describing and using the term-to-term rule, and recognising special sequences.
Term-to-term rules
The term-to-term rule tells you how to get from one term to the next. For 5, 8, 11, 14, … the rule is 'add 3'. To describe a sequence fully you give the first term and the rule.
Key Facts & Formulas
- next term = previous term + common difference
Tips
- Find the difference between consecutive terms first.
- State the first term as well as the rule.
Generating a sequence from a rule
Given a first term and a rule, you can generate a sequence. Starting at 2 with the rule 'multiply by 2' gives 2, 4, 8, 16, … Sequences can also go down, such as 'subtract 4'.
Tips
- Check whether the rule adds, subtracts, multiplies or divides.
- Watch for sequences where the difference changes each time.
Special sequences
Square numbers are 1, 4, 9, 16, 25, … (1², 2², 3², …). Triangular numbers are 1, 3, 6, 10, 15, … where each term adds the next counting number. Recognising these saves time.
Key Facts & Formulas
- square numbers: 1, 4, 9, 16, 25
- triangular numbers: 1, 3, 6, 10, 15
Tips
- Learn the first ten square numbers by heart.
- Triangular numbers grow by +2, +3, +4, … each time.
Revision Checklist
- I can continue a sequence and describe its pattern
- I can find and use a term-to-term rule
- I can generate a sequence from a rule
- I can recognise square and triangular numbers
Frequently Asked Questions
What if the difference is not constant?
Then it is not a linear sequence. Look for a changing pattern in the differences, such as +2, +3, +4, which gives the triangular numbers.
Build strong foundations in Sequences
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