bell quiz. objectives determine whether or not a sequence is arithmetic. write a recursive formula...

Bell Quiz

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

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, …

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.

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

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, …

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, …

Lesson PracticeDetermine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms.

7, 6, 5, 4, …

Lesson PracticeDetermine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms.

10, 12, 15, 19, …

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 .

Arithmetic Sequence

Arithmetic Sequence

• Arithmetic sequences can be represented using a formula

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.

Lesson Practice

Use a recursive formula to find the first four terms of an arithmetic sequence where = – 3 and the common difference d = 4.

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, …

Arithmetic Sequence

• To find the nth term of an arithmetic sequence we can use the formula:

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.

Lesson Practice

Use the rule = 14 + (n – 1)(– 3) to find the 4th and 11th terms of the sequence.

Example 5Finding the nth Term in Arithmetic Sequences

Find the 10th term of the sequences 3, 11, 19, 27, …

Lesson Practice

Find the 10th term of the sequences 1, 10, 19, 28, …

Example 6Finding the nth Term in Arithmetic Sequences

Find the 10th term of the sequences , , , , …

Lesson Practice

Find the 11th term of the sequences , 1, 1, 1 , …

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.

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.