Term-to-term rules
Objective. Describe how each term follows from the previous one.
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- 2. Worked example
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Learn: the key idea
A term-to-term rule describes how to find each new term in a sequence directly from the one before it, rather than from its position. For example, the rule 'add 6 to the previous term' starting from 2 generates 2, 8, 14, 20. Some rules combine two operations, such as 'double the previous term and subtract 1', which starting from 3 generates 3, 5, 9, 17. To find a term-to-term rule from a list of numbers, examine what operation links each term to the one immediately before it.
Worked example
Write the term-to-term rule for the sequence 4, 10, 22, 46, ... and find the next term.
- 1Compare consecutive terms: 10 is not simply 4 plus a constant, since 22 is not 10 plus the same amount.
- 2Check doubling: 4×2=8, close to 10, so test doubling and adding 2: 4×2+2=10.
- 3Confirm the rule with the next pair: 10×2+2=22, and 22×2+2=46. The rule works.
- 4Apply the rule to find the next term: 46×2+2=94.
Answer: Rule: double and add 2; next term is 94
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Practice
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Start practisingCommon mistake. Pupils sometimes describe the position-to-term relationship instead of the term-to-term one, confusing how a term relates to its position with how it relates to the previous term. Always compare a term only with its direct neighbour.
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