Chapter 12 – Sequences and Series Section 1 – Arithmetic Sequences and Series

An Arithmetic Sequence An arithmetic sequence is a sequence of numbers with a difference between consecutive terms that is a constant. This difference is called the common difference. For example: 1, 4, 7, 10,... is an arithmetic sequence with a common difference of 3

The nth term To find the nth term of an arithmetic sequence with a first term of a1 and a common difference of d is given by the formula: an = a1 + (n-1)d

Examples EX 1: Find the 47th term in the arithmetic sequence -4,-1,2,5,... EX 2: Find the first term in the arithmetic sequence for which a19 = 42 and d = -2/3

An Arithmetic Series An arithmetic series is the indicated sum of the terms of an arithmetic sequence. In other words, take an arithmetic sequence and add all the numbers together.

Sum of a Finite Arithmetic Series The sum of the first n terms of an arithmetic series is given by the formula: Sn = (n/2)(a1 + an) Of course, to use this formula you might have to figure out the an term.

Example EX 3: Find the sum of the first 60 terms in the arithmetic series: 9 + 14 + 19 + ... + 304

Assignment Chapter 12, Section 1 pgs 763-765 #18-38E,51,53,55