Arithmetic Sequences Arithmetic Sequence An arithmetic sequence is

Arithmetic Sequences

Arithmetic Sequence An arithmetic sequence is a sequence that has a constant difference between consecutive terms.

Arithmetic Sequence An arithmetic sequence has an additive relationship (common difference) between terms. Terms add or subtract

Examples The arithmetic sequence 74, 67, 60, 53, … represents the amount of money that Tiffany owes her mother at the end of each week. Find the next three terms.

Examples The arithmetic sequence 74, 67, 60, 53, … represents the amount of money that Tiffany owes her mother at the end of each week. Find the next three terms. 74 67 60 53 The common difference is -7 The next three terms are 46, 39, 32 . . .

Examples Find the next four terms of the arithmetic sequence 9. 5, 11. 0, 12. 5, 14. 0, …

Examples Find the next four terms of the arithmetic sequence 9. 5, 11. 0, 12. 5, 14. 0, … 9. 5 11. 0 12. 5 14. 0 The common difference is 1. 5 . .

Writing Arithmetic Sequences (Recursive Rule) Each term in a recursive rule can be expressed in terms of the first term, a 1, the value of the previous term, an-1, and the common difference d. an = an-1 + d

Writing Arithmetic Sequences (Explicit Rule) Each term in an explicit rule can be expressed in terms of the term number, n, first term, a 0, and the common difference d as the rate of change. an = a 0 + d*n

Examples The arithmetic sequence 12, 23, 34, 45, … represents the total number of ounces that a box weighs after each additional book is added. Write a recursive rule and an explicit rule for the sequence. Find the 10 th term in the sequence.

Examples Recursive Rule Explicit Rule an = an-1 + d an = a 0 + d*n a 1 = 12 a 0 = 12 - 11 d = 11 a 0 = 1 an = an-1 + 11 d = 11 an = 1 + 11 n

Examples Find the 10 th term in the sequence. an = 1 + 11 n a 10 = 1 + 11(10) a 10 = 111