Warm up 1. Find the sum of : 2. Find the tenth term of the sequence if an = n2 +1: 4 + 12 + 32 = 48 101

Lesson 11-2 Arithmetic Sequences & Series Objective: To identify an arithmetic sequence and find specific terms in that sequence. Lesson 11-2 Arithmetic Sequences & Series

Arithmetic Sequences Arithmetic sequences increase by a constant amount an = an-1 + d d = 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

Finding any term in an Arithmetic Sequence To find any term in an arithmetic sequence, use the formula an = a1 + (n – 1)d where d is the common difference. Can also be used to find the number of terms in a finite arithmetic sequence.

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 first term is -1, what is the 10th term of an arithmetic sequence? an = a1 + (n – 1)d d = 4 and a1 = -1 a10 = –1 + (10 – 1)4 a10 = 35

Practice If the first 3 terms in an arithmetic progression are 8,5,2 then what is the 16th term? In this progression a = 8 and d = -3. an = a + (n - 1)d a16 = 8 + (16 – 1)(-3) = -37

Sum of an Arithmetic Series 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

Practice Find the sum of each series 1. 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 = 135 2. 6 + 14 + 22 + 30 + …+ 54 = 210 3. 9 + 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81 + 90 = 495