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Algebra Relationships

Learn about linear patterns and how to find algebraic rules for sequences. Explore examples and practice exercises to improve your understanding.

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Algebra Relationships

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  1. Algebra Relationships

  2. Note 1: Linear Patterns Linear Patterns are sequences of numbers where the difference between successive terms is always the same. The general rule for a linear pattern is always of the form: term t = dn + c n is the position of the term in the sequence d is the difference c is a constant

  3. Example 1: Find the rule that generates the sequence Common difference = 5  therefore t = 5n + c Substitute n = 1 into the rule to find c 3 = 5 x 1 + c  therefore c = -2 The rule is: t = 5n - 2

  4. Example 2: Find the rule for the number of toothpicks t needed for the number of n triangles Common difference = 2  therefore t = 2n + c Substitute n = 1 into the rule to find c 3 = 2 x 1 + c  therefore c = 1 The rule is: t = 2n + 1

  5. Note 2: Using Rules for Linear Sequences If the rule for a linear sequence is known, then the values of terms or the term number can be found algebraically. Examples: The rule for a linear sequence is t = 4n -2 Find the 7th term of the sequence t = 4 x 7 – 2 =26 Which term has a value of 74? 74 = 4n -2 76 = 4n n = 19

  6. What is the first term in the sequence that has a value over 151? 4n – 2 > 151 4n > 153 n > 38.25 39th term is the first term greater than 151

  7. Page 74 Exercise A and B

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