12. 1 Arithmetic Sequences and Series 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…”.

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…”. • 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” Arithmetic Sequences

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…”. • Sequence = LIST • Series = SUM Series vs. 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…”. • means the nth term • is the common difference • is the sum of the first n terms. Nth Term: Partial Sum Arithmetic Formulas (you will get these on the quarterly, quiz and exam)

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…”. • 47th term of • 1st term of a sequence whose 19th term is 42 and Example 1: Find the nth term given each of the following

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…”. • 41st term of a sequence in which , • 60th term of Example 1: Find the nth term given each of the following

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…”. • Nth term of a sequence in which and Example 1: Find the nth term given each of the following

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…”. • First 47 terms of the sequence Example 2: Find the nth partial sum given each of the following

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…”. • First 19 terms of a sequence in which and Example 2: Find the nth partial sum given each of the following

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…”. • First 60 terms of Example 2: Find the nth partial sum given each of the following

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…”. • What is the 35th term in the sequence: ? • Determine the sum of the first 25 terms of the arithmetic series • Find the sum of the first 20 terms of the series • What is the 50th term in the sequence ? • An arithmetic sequence has and , find . Example 3: Determine which formula to use for the situation

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…”. • 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 Summary

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. • 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 Summary