9.2 Arithmetic Sequences and Series An arithmetic sequence is a sequence in which each term is obtained by adding a fixed number to the previous term. 5, 9, 13, 17 … is an example of an arithmetic sequence since 4 is added to each term to get the next term. The fixed number added is called the common difference.

9.2 Finding a Common Difference Example Find the common difference d for the arithmetic sequence –9, –7, –5, –3, –1, … Solution d can be found by choosing any two consecutive terms and subtracting the first from the second: d = –5 – (–7) = 2 .

9.2 Arithmetic Sequences and Series nth Term of an Arithmetic Sequence In an arithmetic sequence with first term a1 and common difference d, the nth term an, is given by

9.2 Finding Terms of an Arithmetic Sequence Example Find a13 and an for the arithmetic sequence –3, 1, 5, 9, … Solution Here a1= –3 and d = 1 – (–3) = 4. Using n=13, In general

9.2 Find the nth term from a Graph Example Find a formula for the nth term of the sequence graphed below.

9.2 Find the nth term from a Graph Solution The equation of the dashed line shown Below is y = –.5x +4. The sequence is given by an = –.5n +4 for n = 1, 2, 3, 4, 5, 6 .

9.2 Arithmetic Sequences and Series Sum of the First n Terms of an Arithmetic Sequence If an arithmetic sequence has first term a1 and common difference d, the sum of the first n terms is given by or

9.2 Using The Sum Formulas Example Find the sum of the first 60 positive integers. Solution The sequence is 1, 2, 3, …, 60 so a1 = 1 and a60 = 60. The desired sum is

9.2 Using Summation Notation Example Evaluate the sum . Solution The sum contains the terms of an arithmetic sequence having a1 = 4(1) + 8 = 12 and a10 = 4(10) + 8 = 48. Thus,