Algebra Relationships

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

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 n12345 t

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 Number of triangles (n) Number of toothpicks (t) 357

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

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

Page 74 Exercise A and B