Information about Algebraic Sequences Part B

This is a lesson/slideshow presentation I made for my 8th grade PreAlgebra students.

Example 1 Write the first five terms of the sequence that has an n th term of 6 n + 7 Step 1: Build a table Position 1 2 3 4 5 Term

Write the first five terms of the sequence that has an n th term of 6 n + 7

Step 2 Fill in the table using the position numbers. To find the first term in the sequence, substitute 1 for n . 6 n + 7 6 (1) + 7 6 + 7 = 13 13 Position 1 2 3 4 5 Term

Fill in the table using the position numbers.

Step 2 (continued) Fill in the table using the position numbers. To find the second term in the sequence, substitute 2 for n . 6 n + 7 6 (2) + 7 12 + 7 = 19 13 19 Position 1 2 3 4 5 Term

Fill in the table using the position numbers.

Step 2 (continued) Fill in the table using the position numbers. To find the third term in the sequence, substitute 3 for n . 6 n + 7 6 (3) + 7 18 + 7 = 25 13 19 25 Position 1 2 3 4 5 Term

Fill in the table using the position numbers.

Step 2 (continued) Fill in the table using the position numbers. To find the fourth term in the sequence, substitute 4 for n . 6 n + 7 6 (4) + 7 24 + 7 = 31 13 19 25 31 Position 1 2 3 4 5 Term

Fill in the table using the position numbers.

Step 2 (continued) Fill in the table using the position numbers. To find the fifth term in the sequence, substitute 5 for n . 6 n + 7 6 (5) + 7 30 + 7 = 37 13 19 25 31 37 Position 1 2 3 4 5 Term

Fill in the table using the position numbers.

Example 2 – The Shortcut Write the first five terms of the sequence that has an n th term of -3 n + 11 Step 1: Build a table Step 2: To find the first term in the sequence, substitute 1 for n . -3 n + 11 -3 (1) + 11 -3 + 11 = 8 8 Position 1 2 3 4 5 Term

Write the first five terms of the sequence that has an n th term of -3 n + 11

Example 2 – The Shortcut Write the first five terms of the sequence that has an n th term of -3 n + 11 Step 3: The Shortcut -3 n + 11 8 The coefficient of n is the common difference between terms. -3 -3 -3 -3 5 -1 2 -4 Position 1 2 3 4 5 Term

Write the first five terms of the sequence that has an n th term of -3 n + 11

Example 3 – The Shortcut #2 Write the first five terms of the sequence that has an n th term of -5 n + 9 Step 1: Build a table (this time include zero) Step 2: To find the zero term in the sequence, substitute 0 for n . -5 n + 9 -5 (0) + 9 0 + 9 = 9 9 Position 0 1 2 3 4 5 Term

Write the first five terms of the sequence that has an n th term of -5 n + 9

Example 2 – The Shortcut Write the first five terms of the sequence that has an n th term of -3 n + 11 Step 3: The Shortcut -5 n + 9 9 The coefficient of n is the common difference between terms. -5 -5 -5 -5 4 -6 -1 -11 -16 -5 First five terms Position 0 1 2 3 4 5 Term

Write the first five terms of the sequence that has an n th term of -3 n + 11

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