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Main Idea and Vocabulary
Example 1:Describe and Extend Sequences
Example 2: Describe and Extend Sequences
Example 3: Real-World Example
• sequence
• term
• arithmetic sequence
• Describe the relationships and extend terms in arithmetic sequences.
Describe and Extend Sequences
Describe the relationship between the terms in the arithmetic sequence 7, 11, 15, 19, … Then write the next three terms in the sequence.
Each term is found by adding 4 to the previous term. Continue the pattern to find the next three terms.
Answer: The next three terms are 23, 27, and 31.
19 + 4 = 23 23 + 4 = 27 27 + 4 = 31
+4
7, 11, 15, 19
+4 +4
A. add 9; 55, 64, 53
B. add 11; 57, 68, 79
C. add 13; 59, 72, 85
D. add 15; 61, 76, 91
Describe the relationship between the terms in the arithmetic sequence 13, 24, 35, 46, … Then write the next three terms in the sequence.
Describe and Extend Sequences
Describe the relationship between the terms in the arithmetic sequence 0.1, 0.5, 0.9, 1.3, … Then write the next three terms in the sequence.
Each term is found by adding 0.4 to the previous term. Continue the pattern to find the next three terms.
Answer: The next three terms are 1.7, 2.1, 2.5.
1.3 + 0.4 = 1.7 1.7 + 0.4 = 2.1 2.1 + 0.4 = 2.5
+0.4
0.1, 0.5, 0.9, 1.3
+0.4 +0.4
A. add 0.3; 3.6, 3.9, 4.2
B. add 0.5; 3.8, 4.3, 4.8
C. add 0.8; 4.1, 4.9, 5.7
D. add 0.9; 4.2, 5.1, 6.0
Describe the relationship between the terms in the arithmetic sequence 0.6, 1.5, 2.4, 3.3, … Then write the next three terms in the sequence.
EXERCISE Mehmet started a new exercise routine. The first day, he did 2 sit-ups. Each day after that, he did 2 more sit-ups than the previous day. If he continues this pattern, how many sit-ups will he do on the tenth day?
Make a table to display the sequence.
Each term is 2 times its position number. So, the expression is 2n.
2n Write the expression.
2(10) = 20 Replace n with 10.
Answer: So, on the tenth day, Mehmet will do 20 sit-ups.
A. 8n; 120 seats
B. 8 + n; 23 seats
C. 15n; 120 seats
D. 15 + n; 23 seats
CONCERTS The first row of a theater has 8 seats. Each additional row has eight more seats than the previous row. If this pattern continues, what algebraic expression can be used to find the number of seats in the 15th row? How many seats will be in the 15th row?
