4-7 Arithmetic
Sequences
Objective: To identify and extend
patterns in sequences and represent
in function notation
4-7 Arithmetic Sequences
• Getting Ready on page 276. Solve IT
4-7 Arithmetic Sequences
• A sequence is an ordered list of numbers
that often forms a pattern.
• Each number in the list is called a term of
a sequence.
• Some sequences can be modeled with a
function rule so that you can extend the
sequence to any value.
4-7 Arithmetic Sequences
• Example 1: What are next two terms?
• A. 5, 8, 11, 14 . . .
• B. 2.5, 5, 10, 20 . . .
4-7 Arithmetic Sequences
• An arithmetic sequence: the difference
between consecutive is a constant term,
which is called the constant difference.
• Example 2: Is it an arithmetic sequence?
• A. 3, 8, 13, 18 . . .
• B. 6, 9, 13, 17 . . .
4-7 Arithmetic Sequences
• Sequences are functions and the terms are
the outputs of the function.
A recursive formula is a fn rule that relates
each term of a sequence after the first to the
ones before it.
4-7 Arithmetic Sequences
7, 11, 15, 19 . . .
Find the common difference: FIRST
Write the recursive formula:
Let n = term in sequence
A(n) = the value of the nth term
4-7 Arithmetic Sequences
7, 11, 15, 19 . . .
Let n = term in sequence
A(n) = the value of the nth term
Value of term 1 = A(1) = 7
Value of term 2 = A(2) = A(1) + 4 = 11
Value of term 3 = A(3) = A(2) + 4 = 15
Value of term 4 = A(4) = A(4) + 4 = 19
Value of term 2 = A(2) = A(1) + 4 = 11
Value of term n = A(n) = A(n-2) + 4
4-7 Arithmetic Sequences
The formula for Arithmetic Sequences
A(n) = A(1) + (n – 1) d
Term
number
First term
Common
difference
Term number
4-7 Arithmetic Sequences
The formula for Arithmetic Sequences
A(n) = A(1) + (n – 1) d
Example 4: An online auction works as
shown: Write a formula for it.
Bass
Guitar
Minimu
m Price
$200
Determine common difference:
Bid 1
200
Bid 2
210
A(n) =
Bid 3
220
Bid 4
230
What is 12th bid?
4-7 Arithmetic Sequences
The formula for Arithmetic Sequences
Example 5: An RECURSIVE formula is
represented by: A(n) = A(n – 1) + 12
If the first term is 19, write explicit formula
So A(1) = 19 and adding 12 is common
difference
A(n) = A(1) + (n – 1)d so substitute what you know
A(n) = 19 + (n-1)12 Arithmetic formula
4-7 Arithmetic Sequences
The formula for Arithmetic Sequences
Example 6: An Arithmetic formula is
represented by: A(n) = 32 + (n-1)22
So the first term is ?
So common difference is?
A(n) = A(n – 1) + d so substitute what you know
A(n) =
Recursive formula
4-7 Arithmetic Sequences
HW p. 279 9 – 42 every third