Algebraic Sequences

Algebraic Sequences Obj. Generate an algebraic expression given part of a sequence.

Algebraic Sequence A sequence which has a constant difference between terms. Examples: 1, 5, 9, 13, 17 -7, -1, 5, 11, 17 21, 20, 19, 18, 17

A sequence which has a constant difference between terms.

Examples:

1, 5, 9, 13, 17

-7, -1, 5, 11, 17

21, 20, 19, 18, 17

EXAMPLE 1 Write an expression for the n th term in the sequence 3, 4, 5, 6, 7, …? Step 1 :  Construct a process chart showing the position and the corresponding term. 3 4 5 6 7 +1 +1 +1 +1 Position “ 0” 1 2 3 4 5 n Term

Determine the common difference (the change) of the terms. STEP 2 Common Difference: 1 This is the coefficient of n . 1 n

Reverse the pattern to find the “zero” term. STEP 3 3 4 2 5 6 7 -1 Zero term: 2 Position “ 0” 1 2 3 4 5 n Term

Common Difference: 1 FINISHING IT OFF Zero Term: 2 1 2 n + 2 n +

EXAMPLE 1 Write an expression for the n th term in the sequence 12, 8, 4, 0, -4, …? Step 1 :  Construct a process chart showing the position and the corresponding term. 12 8 4 0 -4 -4 -4 -4 -4 Position “ 0” 1 2 3 4 5 n Term

Determine the common difference (the change) of the terms. STEP 2 Common Difference: -4 This is the coefficient of n . -4 n

Reverse the pattern to find the “zero” term. STEP 3 12 8 16 4 0 -4 +4 Zero term: 16 Position “ 0” 1 2 3 4 5 n Term

Common Difference: -4 FINISHING IT OFF Zero Term: 16 -4 16 -4 n + 16 n +

Practice 4, 9, 14, 19, 24 5n + -1 or 5n - 1 -8, -5, -2, 1, 4 3n + -11 or 3n – 11 7, 1, -5, -11, -17 -6n + 13 -15, -11, -7, -3, 1 4n + -19 or 4n – 19

4, 9, 14, 19, 24

5n + -1 or 5n - 1

-8, -5, -2, 1, 4

3n + -11 or 3n – 11

7, 1, -5, -11, -17

-6n + 13

-15, -11, -7, -3, 1

4n + -19 or 4n – 19