12.2 Arithmetic Sequences and Series

Arithmetic Sequences and Series Arithmetic Sequence: sequence whose consecutive terms have a common difference. Example:3, 5, 7, 9, 11, 13, ... The terms have a common difference of 2. The common difference is the number d. Example: Is the sequence arithmetic? –45, –30, –15, 0, 15, 30 Yes, the common difference is 15 How do you find any term in this sequence? To find any term in an arithmetic sequence, use the formula an = a1 + (n – 1)d where d is the common difference.

Example: Find a formula for the nth term of the arithmetic sequence in which the common difference is 5 and the first term is 3. an = a1 + (n – 1)d a1 = 3 d = 5 an = 3 + (n – 1)5

Example: If the common difference is 4 and the fifth term is 15, what is the 10th term of an arithmetic sequence? an = a1 + (n – 1)d We need to determine what the first term is... d = 4 and a5 = 15 a5 = a1 + (5 – 1)4 = 15 a1 = –1 a10= –1 + (10 – 1)4 a10 = 35

To find the sum of an arithmetic series, we can use summation notation. Which can be simplified to:

Example: Find the sum of the first 100 terms of the arithmetic sequence 1, 2, 3, 4, 5, 6, ... n = 100 = 5050

12.2 Arithmetic Sequences and Series