1. Warm Up Write the first 4 terms of each sequence:
1. 𝑡 1 =6 𝑡 𝑛 = 1 2 𝑡 𝑛−1 +4
2. 𝑡 1 =−2 𝑡 𝑛 = 𝑡 𝑛−
3. 𝑡 1 =3𝑥 𝑡 𝑛 = 𝑡 𝑛−1 +2 𝑛−1
4. 𝑡 1 =3 𝑡 𝑛 = −1 𝑛 ∙5 𝑡 𝑛−1
5. Write an explicit and a recursive formula
for the sequence 9, -18, 36, -72, ...
6, 7, 7.5, 7.75
−2, 7, 52, 2707
3𝑥, 3𝑥+2, 3𝑥+4 2 , 3𝑥+8 6
3, 15, −75, −375
𝑡𝑛=9∙ −2 𝑛−1
𝑡 1 =9
𝑡 𝑛 = −2𝑡 𝑛−1

2. 13.3 Arithmetic & Geometric Series and Their Sums:
13.3 Arithmetic & Geometric Series and Their Sums

7. Classwork
Find the sum of each arithmetic series. 1. 𝐹𝑖𝑛𝑑 𝑆 200: 𝑡 1 =18, 𝑡 200 = 𝐹𝑖𝑛𝑑 𝑆 25: … …+99 Find the sum of the geometric series. 4. Find 𝑆 8 : …+6561 Find a formula for 𝑡 𝑛 . Then give a recursive definition for 𝑆 𝑛 …

8. 1. 𝐹𝑖𝑛𝑑 𝑆 200: 𝑡 1 =18, 𝑡 200 =472
= 200(18+472) 2
=49,000
2. 𝐹𝑖𝑛𝑑 𝑆 25: …
𝑡 25 =17+ 25−1 8=209
𝑡 𝑛 = 𝑡 1 + 𝑛−1 𝑑
= 25(17+209) 2
=2,825

9. …+99
𝑛=25
𝑡 𝑛 = 𝑡 1 + 𝑛−1 𝑑
99=3+ 𝑛−1 4
= 25(3+99) 2
=1,275
4. Find 𝑆 8 : …+6561
= 3(1− 3 8 ) 1−3
=9,840

10. 𝑡𝑛=1∙ 3 𝑛−1 𝑡𝑛= 𝑡 1 ∙ 𝑟 𝑛−1 𝑆 0 =0 𝑆 𝑛 = 𝑆 𝑛−1 + 𝑡 𝑛 𝑆 0 =0
Find a formula for 𝑡 𝑛 . Then give a recursive definition for 𝑆 𝑛 . …
𝑡𝑛= 𝑡 1 ∙ 𝑟 𝑛−1
𝑡𝑛=1∙ 3 𝑛−1
𝑆 0 =0
𝑆 𝑛 = 𝑆 𝑛−1 + 𝑡 𝑛
𝑆 0 =0
𝑆 𝑛 = 𝑆 𝑛−1 + 3 𝑛−1

11. Homework
Page 489 #1-19 odds, 27, 33