Algebraic Sequences Algebraic Sequence l A pattern of

Algebraic Sequences

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

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 Term “ 0” 1 2 3 3 4 +1 4 6 5 +1 7 +1 n

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

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

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

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 Term “ 0” 1 2 12 3 8 -4 4 0 4 -4 -4 5 -4 -4 n

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

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

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

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