Objectives Module 20 Arithmetic Sequences 1. Find the common difference for an arithmetic sequence. 2. Write terms of an arithmetic sequence.. 3. Use a recursive formula for an arithmetic sequence. 4. Use an explicit formula for an arithmetic sequence. Why do we study arithmetic sequences? In some data, there is a common difference between the terms. For example, the numbers of seats in the rows of a theater, the height of a plant during a sequence of observation time points, the balance of an investment in which you earn a fixed increment, etc. These application problems can be analyzed by using the properties of arithmetic sequences. (1) What is an Arithmetic Sequence? An arithmetic sequence is a sequence in which each term after the first differs from the preceding term by a constant amount, called the common difference. (a, a +d, a + 2d,, a + (n-1)d,...) Example 1: a = 100 and d 7. Write the first 5 terms Let d represent the common difference. Explicit (nth term) formula: an a + d(n - 1) d = a-a = az-azan+1-an Example 2: Is each sequence arithmetic? If so, find the common difference. (1,2,4,8,16,...) (-3, 1, 5, 9, 13, ...) 1 (8, 5, 2, 0, -2, -4,...)