Chapter 8: Sequences and Series Lesson 1: Formulas for Sequences Mrs. Parziale

Vocabulary: sequence: a function whose domain is the set of consecutive integers greater than or equal to k. (usually k = 1). Arithmetic Sequences – a sequence in which the difference between consecutive terms is constant. (add or subtract the same value)

Formulas for Arithmetic Sequences Explicit Formulas – formula which shows the nth term of a sequence in terms of n. n th term first term constant difference

Formulas for Arithmetic Sequences Recursive Formulas – formula which the first term or first few terms are given, and then the nth tem is expressed using the preceding term(s). first term constant difference previous term n th term

Example 1: Write a recursive and explicit formula for the following arithmetic sequences: a) 1, 5, 9, 13, 17, b) 5, -1, -7, -13,.....

Vocabulary Geometric Sequences – a sequence in which the ratio of consecutive terms is constant. (multiply or divide by the same value)

Formulas for Geometric Sequences Explicit Formulas – formula which shows the nth term of a sequence in terms of n. n th term first term constant ratio

Formulas for Geometric Sequences Recursive Formulas – formula which the first term or first few terms are given, and then the nth tem is expressed using the preceding term(s). first term constant ratio previous term n th term

Example 2: Write a recursive and explicit formula for the following geometric sequences: a) 3, 6, 12, 24, 48,.... b) 4, -12, 36, -108,.....

Example 3: A.Find the 49 th term in the arithmetic sequence 8, 15, 22, 29, … Difference = Explicit: a n = Recursive:

Example 4: A.Give the 7 th term in the geometric sequence 16, 24, 36, … Ratio = Explicit: g n = Recursive:

Closure: A particular car depreciates 25% in value each year. Suppose the original cost is $14,800. a) Find the value of the car in its second year (ie. after 1 year). b) Write an explicit formula for the value of the car in its nth year. c) In how many years will the car be worth about $1000?