By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

*12. 1 Arithmetic Sequences and Series

Arithmetic Sequences

*What is the next number in each sequence?

*These are all ARITHMETIC sequences because each term ADD or SUBTRACTS the same amount.

*This amount is called the “common difference”

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Series vs. Sequence

*Sequence = LIST

*Series = SUM

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Arithmetic Formulas (you will get these on the quarterly, quiz and exam)

* means the nth term

* is the common difference

* is the sum of the first n terms.

Nth Term:

Partial Sum

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Example 1: Find the nth term given each of the following

A. 47th term of

B. 1st term of a sequence whose 19th term is 42 and

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Example 1: Find the nth term given each of the following

C. 41st term of a sequence in which ,

D. 60th term of

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Example 1: Find the nth term given each of the following

E. Nth term of a sequence in which and

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Example 2: Find the nth partial sum given each of the following

A. First 47 terms of the sequence

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Example 2: Find the nth partial sum given each of the following

B. First 19 terms of a sequence in which and

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Example 2: Find the nth partial sum given each of the following

C. First 60 terms of

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Example 3: Determine which formula to use for the situation

A. What is the 35th term in the sequence: ?

B. Determine the sum of the first 25 terms of the arithmetic series

C. Find the sum of the first 20 terms of the series

D. What is the 50th term in the sequence ?

E. An arithmetic sequence has and , find .

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Summary

1. What is the 25th term in the sequence 8, 11, 14, 17, … ?

2. What is the sum of the first 25 terms in the sequence 8, 11, 14, 17, … ?

3. What is the 50th term for the sequence which has ?

4. What is if a sequence has

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of “I have…who has…”.

Summary

*What is the 25th term in the sequence 8, 11, 14, 17, … ?

*What is the sum of the first 25 terms in the sequence 8, 11, 14, 17, … ?

*What is the 50th term for the sequence which has ?

*What is if a sequence has

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the nth term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion of a graphic organizer.