The document discusses arithmetic sequences and provides examples of determining whether a sequence is arithmetic, writing recursive and explicit formulas for arithmetic sequences, and finding terms of arithmetic sequences given a formula. It includes examples of identifying the common difference of an arithmetic sequence, writing recursive and explicit formulas, and using formulas to find specific terms. Formulas shown include the recursive formula A(n) = A(n-1) + d and explicit formula A(n) = A(1) + (n-1)d for an arithmetic sequence.

1. REVIEW
Create a line graph for the following interval
( -6, 3] or [7, - 11)
ARITHMETIC AND GEOMETRIC SEQUENCES

2. ARITHM
ETIC
AND
GEOM
ETRIC
SEQUENCES
ARITHMETIC AND GEOMETRIC SEQUENCES

3. SEQUENCE
A sequence is an ordered list of numbers that often form a
pattern. Each number in the list is called a term of
sequence.
Describe the pattern in the following sequences and write the
next two terms
a.) 5,11,17,23 c.) 400, 200, 100, 50
b.) 2, -4, 8, -16 d.) -15, -11, -7, -3
ARITHMETIC AND GEOMETRIC SEQUENCES

4. ARITHMETIC SEQUENCE
In an arithmetic sequence, the difference between
consecutive terms is constants. This difference is called
the common difference.
Example: 3, 8, 13, 18
ARITHMETIC AND GEOMETRIC SEQUENCES

5. ARITHMETIC SEQUENCE
Tell whether the sequence is arithmetic. If it is, what is
the common difference?
a.) 8, 15, 22, 30 b.) 7, 9, 11, 13
c.) 10, 4, -2, -8 d.) 2, -2, 2, -2
ARITHMETIC AND GEOMETRIC SEQUENCES

6. RECURSIVE AND EXPLICIT FORMULA
Let n= the term number in the sequence
Let A(n) = the value of the nth term of the sequence
Let d= the common difference
Recursive Formula Explicit Formula
A(n) = A( n – 1) + d A(n) = A(1) + (n – 1)d
ARITHMETIC AND GEOMETRIC SEQUENCES

7. RECURSIVE AND EXPLICIT FORMULA
Example:
An arithmetic sequence is represented by the recursive
formula A(n) = A (n – 1) + 12. If the first sequence is 19,
write the explicit formula.
ARITHMETIC AND GEOMETRIC SEQUENCES

8. RECURSIVE AND EXPLICIT FORMULA
An arithmetic sequence is represented by the explicit
formula A(n) = 32 + (n – 1) (22). What is the recursive
formula?
ARITHMETIC AND GEOMETRIC SEQUENCES

9. RECURSIVE AND EXPLICIT FORMULA
1.) Write a recursive formula for the sequence: 99, 88, 77,
66
2.) Write a recursive formula for the explicit formula:
A(n) = 5 + (n -1) (3)
3.) Find the 2nd
, 4th
, and 11th
term: A(n) = - 3+ (n – 1) (5)
ARITHMETIC AND GEOMETRIC SEQUENCES

10. RECURSIVE AND EXPLICIT FORMULA
Write a recursive and an explicit formula for the
arithmetic sequence:
9, 7, 5, 3, 1
Find the 7th
and 11th
term
ARITHMETIC AND GEOMETRIC SEQUENCES

11. RECURSIVE AND EXPLICIT FORMULA
Find the second, third, and fourth terms of the sequence.
Then write the explicit formula that represents the
sequence
A(n) = A (n – 1) – 1 ; A(1) = 8
ARITHMETIC AND GEOMETRIC SEQUENCES