Download Arithmetic Sequences

Warm Up
State the pattern for each step.
• 3, 6, 9, 12, 15, 18, 21, 24, …
• 25, 20, 15, 10, 5, 0, -5, -10, …
• -21, 3, 27, 51, 75, 99, 123, …
Arithmetic Sequence
An arithmetic sequence is defined as a sequence
in which there is a common difference
between consecutive terms.
26,  21,  16,  11,  6, . . .
Is the given sequence arithmetic? If so, identify the
common difference.
1.
2.
3.
4.
5.
6.
2, 4, 8, 16, …
4, 6, 12, 18, 24, …
2, 5, 7, 12, …
48, 45, 42, 39, …
1, 4, 9, 16, …
10, 20, 30, 40, …
Arithmetic Sequence Formula
The 1st number in
the sequence.
The common
difference.
an = a1 + (n – 1) • d
The “nth” number
in the sequence.
Ex. a5 is the 5th
number in the
sequence.
The same as the n
in an. If you’re
looking for the 5th
number in the
sequence, n = 5.
Example 1:
an = a1 + (n – 1) • d
Given the sequence -4, 5, 14, 23, 32, 41, 50,…,
find the 14th term.
Example 2:
an = a1 + (n – 1) • d
Given the sequence 6, 10, 14, 18, 22, 26,…, find
the 17th term.
Example 3:
an = a1 + (n – 1) • d
Given the sequence 81, 80.5, 80, 79.5, 70,…, find
the 9th term.
Example 4:
an = a1 + (n – 1) • d
Given the sequence 79, 75, 71, 67, 63,…, find
the term number that is -169.
Example 5:
an = a1 + (n – 1) • d
Suppose you are saving up for a new gaming
system. You have 100 dollars this year, and
you plan to add 33 dollars each of the
following years. How much money will you
have in 7 years?
Arithmetic Mean
• Used to find the missing term of an arithmetic
sequence
• Add the numbers and divide by two.
Find the missing term of the arithmetic
sequence.
84, ____, 110
Find the missing term of the arithmetic
sequence.
24, ____, 57