1. OBJECTIVE
We will find the missing terms in an arithmetic and a geometric sequence by looking for a pattern and using the formula.

2. 1. 25th term in the sequence 3, 7, 11, 15, 19 …
Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d
1. 25th term in the sequence 3, 7, 11, 15, 19 …

3. 2. Find the 62nd, 200th, 20th term in the sequence 3, 7, 11, 15, 19 …
Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d
2. Find the 62nd, 200th, 20th term in the sequence 3, 7, 11, 15, 19 …

4. 3. What is the 47th term in the sequence?
Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d
3. What is the 47th term in the sequence?
21, 15, 9, 3, . . .

5. 4. What is the 80th term in the sequence?
Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d
4. What is the 80th term in the sequence?
21, 15, 9, 3, . . .

6. ARITHMETIC SEQUENCE -is a numerical pattern with a common difference.
- have an addition or subtraction rule.

7. Vocabulary
Sequence- a set of numbers
{1, 3, 5, 7, …}
Terms- each number in a sequence
Common Difference- the number added to find the next term of an arithmetic sequence.

8. 3, 7, 11, 15, 19 …
What is the common difference? +4
What is the seventh term in the sequence?
3, 7, 11, 15, 19 , 23, 27

9. look at the PATTERN for the preceding terms
To find the next term…
look at the PATTERN for the preceding terms
Ex. 1, 5, 9, ___, ____
Pattern: Add 4

10. FIND the 5th term in the sequence -28, -17, -6, 5…
Find the common difference by subtracting the 2nd term and the 1st term: +11
Add 11 to the 4th term in the sequence: = 16
ANSWER: The 5th term is 16

11. FIND the 10th term in the sequence -28, -17, -6, 5…
Find the common difference by subtracting the 2nd term and the 1st term: +11
Add 11 from the 4th to the 10th term in the sequence:
-28, -17, -6, 5, 16, 27, 38, 49, 60, 71
ANSWER: The 10th term is 71

12. GEOMETRIC SEQUENCE
The ratio of successive terms in a geometric sequence is a constant called the common ratio, denoted by r.

13. Find the common ratio and the 8th term of the following:
1) 1, 2, 4, 8, 16, ...
2) 27, 9, 3, 1, 1/3, ...
3) 3, 6, 12, 24, 48, ...
4) 1/2, -1, 2, -4, 8, ...

14. This is important! Arithmetic formula:
an  =  a1  +  (n - 1)d
an  is the nth term, a1 is the first term, and d is the common difference.
Geometric formula:          
an = a1 . r (n - 1)
an is the nth term, a1 is the first term, and r is the common ratio.

15. 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, . . .

16. 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?)

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