Algebraic Sequences Part B
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The document discusses determining the terms of an algebraic sequence given a formula for the nth term. It provides examples of writing the first five terms of sequences where the nth term is: 1) 6n + 7, with terms 13, 19, 25, 31, 37 2) -3n + 11, with terms 8, 5, 2, -1, -4 3) -5n + 9, with terms 9, 4, -1, -6, -11 In each case, the nth term formula is used to generate the terms by substituting in the position numbers from 1 to 5 for n.
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This document discusses arithmetic sequences and their properties. It defines an arithmetic sequence as a sequence where the difference between consecutive terms is constant. It provides the formula for the nth term of an arithmetic sequence as an = a1 + (n-1)d, where a1 is the first term, n is the term number, and d is the common difference. It gives examples of finding specific terms and summarizing sequences. It also discusses the arithmetic mean and arithmetic sum formulas.Arithmetic sequence
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Algebraic Sequences Part B
- 1. Algebraic Sequences Part B Obj: Determine the sequence of the n th term of an algebraic expression.
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. 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
- 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 -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
- 10. 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
- 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 -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