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
3.
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
4.
Determine the common difference (the change) of the terms. STEP 2 Common Difference: 1 This is the coefficient of n . 1 n
5.
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
6.
Common Difference: 1 FINISHING IT OFF Zero Term: 2 1 2 n + 2 n +
7.
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
8.
Determine the common difference (the change) of the terms. STEP 2 Common Difference: -4 This is the coefficient of n . -4 n
9.
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
10.
Common Difference: -4 FINISHING IT OFF Zero Term: 16 -4 16 -4 n + 16 n +