1. Algebraic Sequences

2. A pattern of numbers with a constant difference between terms.
Algebraic Sequence
A pattern of numbers with a constant difference between terms.
Examples:
1, 5, 9, 13, 17
-7, -1, 5, 11, 17
21, 20, 19, 18, 17

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

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

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

6. Finishing it Off
Common Difference: 1
Zero Term: 2
n + 1 2
n + 2

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

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

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

10. -4n + 16 16 -4 n + Zero Term: 16 Finishing it Off
Common Difference: -4
Zero Term: 16
n + -4 16
-4n + 16

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