Lesson 3-6 Arithmetic Sequences Obj: The student will be able to 1) Recognize and extend an arithmetic sequence 2) Find a given term of an arithmetic sequence HWK: p 209 9-12 all, 13-15 all, 16-26 even, 28-32 all Vocab: 1) sequence 2) term 3) arithmetic sequence 4) common difference

The variable “a” is used to represent the terms in a sequence The variable “a” is used to represent the terms in a sequence. The variable “a₉” is the ninth term of a sequence. To designate any term, or the nth term, in a sequence, write “ 𝑎 𝑛 ” where n can be any number. To find the a term in an arithmetic sequence, add d to the previous term Finding a Term of an Arithmetic Sequence: The nth term of an arithmetic sequence with common difference d is 𝑎 𝑛 = 𝑎 𝑛−1 + d

Determine whether each sequence appears to be an arithmetic sequence Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms. Ex 1) 12, 8, 4, 0, ….. Ex 2) 1, 4, 9, 16, ……..

Ex 3) − 3 4 , − 1 4 , 1 4 , 3 4 , …..

To find the nth term when n is a large number, you need an equation or rule. Look for a pattern in this sequence: 3, 5, 7, 9, …. Starts with 3, common difference is 2 1st 2nd 3rd 4th … 𝑎 1 𝑎 2 𝑎 3 𝑎 4 … Words Numbers Algebra 1st term 3 𝑎 1 2nd term = 1st term plus 1 common difference 3 + (1) 2 = 5 𝑎 1 + 1d 3rd term = 1st term plus 2 common differences 3 + (2) 2 = 7 𝑎 1 + 2d 4th term = 1st term plus 3 common differences 3 + (3) 2 = 9 𝑎 1 + 3d ……. …….. nth term = 1st term plus (n-1) common differences 3 + (n-1) 2 𝑎 1 + (n – 1)d

Finding the nth term of an Arithmetic Sequence The nth term of an arithmetic sequence with common difference d and first term 𝑎 1 is 𝑎 𝑛 = 𝑎 1 + (n – 1)d

Find the indicated term of each arithmetic sequence. Ex 4) 5, 2, -1, -4, …. Find the 22nd term Ex 5) 𝑎 1 = 7, d = 3 Find the 15th term

Ex 6) 11, 5, -1, -7, ….. Find the 60th term

Ex 7) The odometer on a car reads 60,473 on day 1 Ex 7) The odometer on a car reads 60,473 on day 1. Every day, the car is driven 54 miles. If this pattern continues, what is the odometer reading on day 20?

Ex 8) Each time a truck stops, it drops off 250 pounds of cargo Ex 8) Each time a truck stops, it drops off 250 pounds of cargo. After stop 1, its cargo weighed 2000 pounds. How much does the load weigh after stop 6?