Algebraic Sequences

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

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

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

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

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

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

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

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

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

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