Algebra Relationships

Note 1: Linear PatternsLinear 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 + cn is the position of the term in the sequenced is the differencec 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 c3 = 5 x 1 + c therefore c = -2

The rule is: t = 5n - 2

n 1 2 3 4 5t 3 8 13 18 23

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 c3 = 2 x 1 + c therefore c = 1

The rule is: t = 2n + 1

Number of triangles (n) 1 2 3 4 5Number of toothpicks

(t)3 5 7

Note 2: Using Rules for Linear Sequences

Examples:The rule for a linear sequence is t = 4n -2Find the 7th term of the sequence

t = 4 x 7 – 2=26

Which term has a value of 74?74 = 4n -276 = 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 > 38.25

39th term is the first term greater than 151

Page 74Exercise A and B