1. All you ever need to know about Sequences and Series

2. Definitions
A sequence - a function whose domain is a set of consecutive integers. If the domain is not specified then it is understood that it starts with 1.
An arithmetic sequence is a sequence with the difference between two consecutive terms constant.  The difference is called the common difference.
A geometric sequence is a sequence with a common ratio, r.
i.e. The ratio of successive terms in a geometric sequence is a constant called the common ratio, denoted r.

3. Let's play guess the sequence!: I give you a
sequence and you guess the type. 
3, 8, 13, 18, 23, . . .  
1, 2, 4, 8, 16, . . .
24, 12, 6, 3, 3/2, 3/4, . . . 
55, 51, 47, 43, 39, 35, . . .
2, 5, 10, 17, . . .  
1, 4, 9, 16, 25, 36, . . .

4. Answers! 1) Arithmetic, the common difference d = 5
2) Geometric, the common ratio r = 2
3) Geometric, r = 1/2
4) Arithmetic, d = -4
5) Neither, why? (How about no common difference or ratio!)
6) Neither again! (This looks familiar, could it be from geometry?)

5. Sample problems: 1) un = 3n + 2 2) un = n2 + 1 3) un = 3(2)n
Find the first four terms and state whether the sequence is arithmetic, geometric, or neither.
1)  un = 3n + 2   
2) un = n2 + 1  
3)  un = 3(2)n                              

6. Answers:
1)  un = 3n + 2  
To find the first four terms, in a row, replace n with 1, then 2, then 3 and 4
Answer: 5, 8, 11, 14         
The sequence is arithmetic!  d = 3

7. 2) un = n2 + 1
To find the first four terms, do the same as above!
Answer:  2, 5, 10, 17         
The sequence is neither.  Why?

8. 3)  un = 3(2)n 
Ditto for this one ( got it by now?)
Answer:  6, 12, 24, 48        
The sequence is geometric with r = 2

9. Arithmetic Sequences and Series

10. Vocabulary of Sequences (Universal)

11. Given an arithmetic sequence withx 38 15 NA -3
X = 80

12. 9 x
633 NA 24
X = 27

13. -6 29 20 NA x

14. How do you find the sum of an Arithmetic Sequence?

15. A sequence is defined by un= 68-5n.
Prove that the sequence is arithmetic.
Find the first term and d.
Find the 37th term
Find the sum of 37 terms.

16. Find n for the series in which5 y x
440 3
Graph on positive window
X = 16

17. Arithmetic Series Practice
1. Find the sum of ….. to 20 terms
2. Find the sum of the first 10 terms of the pattern represented by 2k + 5
3. Find the sum of the first 50 multiples of 11

18. Each section of a soccer stadium has 44 rows with 22 seats in the first row, 23 in the second row, 24 in the third row, and so on. How many seats are there in:
Row 44
Each section
The stadium which has 25 sections.