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Discovering Number Patterns: Rules, Sequences, and Finding Terms

This guide explores number patterns and sequences, detailing how to identify the rule for progression from one term to the next. It demonstrates practical examples, such as calculating the next number in various patterns and deriving the nth term formula. By applying the outlined methods, you can efficiently find any term in the sequence without continuous addition. Specific examples, including arithmetic sequences, will help clarify how to derive the 20th or 100th term, making it perfect for students and enthusiasts of mathematics seeking deeper understanding.

stevenmcguire
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Discovering Number Patterns: Rules, Sequences, and Finding Terms

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  1. Number Patterns

  2. Number patterns Key words: Pattern Sequence Rule Term Formula

  3. 5 12 19 26 33 What is the next number? 30 What next? 37 What is the rule? Add 7

  4. 8 11 14 17 20 What is the next number? 23 What next? 26 What is the rule? Add 3

  5. 8 11 14 17 20 How can we find the 20th term, or the 100th term, without having to keep on adding 3s?

  6. 8 11 14 17 20 We need to find a formula for the nth term.

  7. 8 11 14 17 20 Start by drawing a table:

  8. The formula has 2 parts:(i) difference x term numberin this case: 3n

  9. The formula has 2 parts:(i) difference x term numberin this case: 3n(ii) plus term “0” (the term before the first one!)in this case: 5

  10. 8 11 14 17 20 So for this pattern, nth term = 3n + 5 20th term = 3x20 + 5 = 65 100th term = 3x100 +5 = 305

  11. 7 9 11 13 5 8 11 14 6 10 14 18 20 30 40 50 18 36 54 72 Nth term: 20th term: 2n + 5 45 3n + 2 62 4n + 2 82 10n + 10 210 18n 360 For each pattern, finda) the rule to get from one term to the nextb) the next 3 termsc) the nth term formulad) the 20th term.

  12. JRElse 2004

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