Algebra 1: Unit 5 - Day 2 Notes Arithmetic Sequences as Linear Functions !Definitions:

!1. Determine whether each sequence is an arithmetic sequences. Explain.

!2. Find the next four terms of the arithmetic sequence 1, 10, 19, 28, . . . !!!Each term in an arithmetic sequence can be expressed in terms of the first term ! and the common difference d.

Sequence: A list of numbers in a particular order. Each number in a sequence is called a

term. The first term is symbolized by , the second term is , and so on.

Example:

4 6 8 10 12

a1 a2

a1 a2 a3 a4 a5

Arithmetic Sequence: A sequence in which each term after the first is found by

____________a constant, called the common difference ! , to the previous term.

!Example:

43, 37, 31, 25, 19, . . .

!What is the common difference ( ! )?

d

d

a. -15, -13, -11, -9, . . . !!!!!!!

b. � !

!!!

78,58,18,− 5

8, . . .

a1

! Term of an Arithmetic Sequence

!3. For the following sequence -8, -11, -14, -17 . . . !a. Write an equation for the � term of the arithmetic sequence. !!!b. Graph the first five terms in the sequence. !!! !

c. Find the 12th term of the sequence. !!!! d. Which term of the sequence is -182? !!!!!

Term Symbol

first term 3

second term 3+3=6

third term 3+2(3)=9

fourth term 3+3(3)=12

3+(n-1)3 !____________________

!an

! a1+ d!a2

! a1+ 2d!a3

In terms of ! and !a1 d

termnth

! a1+ 3d!a4

! a1!a1

Example !�3,6,9,12...

nth

The � term of an arithmetic sequence with the first term � and common difference � is given by !

� !where n is a positive number.

nth a1 d

an = a1+ n−1( )d

nth

4. The arithmetic sequence 12, 23, 34, 45, . . . represents the total number in ounces that a bag weighs after each additional newspaper is added. !

a. Write a formula to represent this sequence. !!!!!b. Write an equation in function notation to represent this sequence. !!!!c. Graph the function. !

!!!!d. Determine the domain and range. !