Sequences A sequence is a function whose domain

Sequences A sequence is a function whose domain is a set of consecutive whole numbers. So the domain in any sequence is {1, 2, 3, 4…} The values in the range are called the terms of the sequence. A sequence can be specified by an equation or a rule.

Arithmetic Sequence A sequence of terms that have a common difference between them

Determine if the sequence is arithmetic. Example: -22, -15, -8, -1, … Arithmetic d=7

Determine if the sequence is arithmetic. Example: ½, ¼, 1/8, 1/16, … Not Arithmetic

Determine if the sequence is arithmetic. Example: 7, 4, 1, -2, -5 Arithmetic d = -3

Explicit Formula used to find the th n term of a sequence

Explicit Formula for Arithmetic Sequence

Find the common difference, the explicit formula, and the tenth term. 3, 9, 15, 21, … d=6 an = 6 n – 3 a 10 = 57

Find the common difference, the explicit formula, and the twentieth term. 7, 4, 1, -2, …

Applications • The marching band has 14 marchers in the front row, 16 in the second row, 20 in the fourth row, and so on. How many marchers are in the 15 th row?

Applications • Several friends want to go on a rafting trip. The cost of the trip person is in the chart. Passenger 1 2 3 4 s Cost $75 $100 $125 $150 • How much would it cost for 9 people to go?

Applications • A bag of cat food weighs 18 pounds at the beginning of day 1. Each day, the cats are fed 0. 5 pounds of food. How much does the bag of cat food weigh at the beginning of day 30?

Recursive Formula A recursive rule for a sequence defines the nth term by relating it to one or more previous terms.

Recursive Formula for Arithmetic Sequence

Find the first four terms of the sequence. Example: a 1 = 3 an = an-1 + 2 3, 5, 7, 9

Write the recursive formula for the following sequence: • 3, 6, 9, 12… • What are the next 3 terms?