bell quiz. objectives determine whether or not a sequence is arithmetic. write a recursive formula...
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Bell Quiz
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Objectives
• Determine whether or not a sequence is arithmetic.
• Write a recursive formula for an arithmetic sequence.
• Find the nth term of an arithmetic sequence
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Sequence
• Sequences of numbers can be formed using a variety of patterns and operations.
• A sequence is a list of numbers that follow a rule– each number in the sequence is called a term of the
sequence. • Here are a few examples of sequences:
• 1, 3, 5, 7, …• 7, 4, 1, –2, …• 2, 6, 18, 54, …• 1, 4, 9, 16, …
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Arithmetic Sequence
• In the previous examples, the first two sequences are a special type of sequence called an arithmetic sequences.
• An arithmetic sequence is a sequence that has a constant difference between two consecutive terms called the common difference.
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Arithmetic Sequence
• To find the common difference, choose any term and subtract the previous term.
• In the first sequence, the common difference is 2.
• In the second sequence, the common difference is –3
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Example 1Recognizing Arithmetic Sequences
Determine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms.
7, 12, 17, 22, …
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Example 2Recognizing Arithmetic Sequences
Determine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms.
3, 6, 12, 24, …
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Lesson PracticeDetermine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms.
7, 6, 5, 4, …
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Lesson PracticeDetermine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms.
10, 12, 15, 19, …
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Arithmetic Sequence
• The first term of a sequence is denoted as , the second term as , the third term , and so on.
• The nth term of an arithmetic sequence is denoted as .
• The term preceding is denoted .• For example, if n = 6 then the term preceding
is or .
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Arithmetic Sequence
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Arithmetic Sequence
• Arithmetic sequences can be represented using a formula
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Example 3Using a Recursive Formula
Use a recursive formula to find the first four terms of an arithmetic sequence where = – 2 and the common difference d = 7.
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Lesson Practice
Use a recursive formula to find the first four terms of an arithmetic sequence where = – 3 and the common difference d = 4.
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Arithmetic Sequence
• A rule for finding any term in an arithmetic sequence can be developed by looking at a different pattern in the sequence 7, 11, 15, 19, …
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Arithmetic Sequence
• To find the nth term of an arithmetic sequence we can use the formula:
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Example 4Finding the nth Term in Arithmetic Sequences
Use the rule = 6 + (n – 1)2 to find the 4th and 11th terms of the sequence.
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Lesson Practice
Use the rule = 14 + (n – 1)(– 3) to find the 4th and 11th terms of the sequence.
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Example 5Finding the nth Term in Arithmetic Sequences
Find the 10th term of the sequences 3, 11, 19, 27, …
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Lesson Practice
Find the 10th term of the sequences 1, 10, 19, 28, …
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Example 6Finding the nth Term in Arithmetic Sequences
Find the 10th term of the sequences , , , , …
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Lesson Practice
Find the 11th term of the sequences , 1, 1, 1 , …
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Example 7Application: Seating for a Reception
The first table at a reception will seat 9 guest while each additional table will seat 6 more guests. a. Write a rule to model the situation.
b. Use the rule to find how many guests can be seated with ten tables.
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Lesson Practice
Flowers are purchased to put on tables at a reception. The head table needs to have 12 flowers and the other tables need to have 6 flowers eacha. Write a rule to model the situation.
b. Use the rule to find the number of flowers needed for 15 tables.