1. Section 9.3 Arithmetic Sequences
Algebra II
Section 9.3
Arithmetic Sequences

2. Warm Up
Find the 5th term in the sequence. #1 𝑎 𝑛 =𝑛+6 #2 𝑎 𝑛 =4−𝑛 #3 𝑎 𝑛 =3𝑛+4

3. More Warming
Write a possible explicit term for The nth term of the sequence. #4 4,5,6,7,8,… #5 −3,−1,1,3,5,… #6 3 2 ,2, 5 2 ,3, 7 2 ,…

4. Find the difference
Arithmetic sequence- terms in the sequence have a common difference
2,5,8,11,14… common difference 3
4,8,16,32,64 no common difference

5. Try these!
Pg #2-4

6. For an arithmetic sequence, the nth term is given by the formula
𝒂 𝒏 = 𝒂 𝟏 + 𝒏−𝟏 𝒅
𝑎 1 𝑖𝑠 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚
𝑑 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝑛 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎 𝑡𝑒𝑟𝑚

7. What is 𝑎 1 ?
What is d
What is n?

8. Try these! Pg

9. Find the missing terms in the sequence.
−3, ____,_____,______,______,27
We know 27 is the 6th term so n=6
We know 𝑎 1 =−3
Find d in the formula.
Fill in the missing numbers and solve for d.
Use d to find the missing terms.

10. Try these!
Pg #8-10

11. Given 𝑎 3 =22, 𝑎 9 =40
Find the 12th term
22= 𝑎 1 +2𝑑 and 40= 𝑎 1 +8𝑑
Use a system of equations to find d
22= 𝑎 1 +2𝑑
40= 𝑎 1 +8𝑑

12. Try these!
Pg #11-16

13. Homework/Classwork
Pg. 648 #21-36,52-56