Download Sequences & series

Warm Up
State the pattern for each sequence
• 3, 6, 9, 12, 15, 18, 21, 24, …
• 25, 20, 15, 10, 5, 0, -5, -10, …
• -21, 3, 27, 51, 75, 99, 123, …
Unit 7 – Sequences & Series
A sequence is a list of numbers that
follow a particular pattern.
Each number in the list is called a
term.
Arithmetic Sequence
An arithmetic sequence is defined as a
sequence in which there is a common
difference between consecutive terms.
A common difference is the number added or
subtracted each time.
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, 79,…, 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.
a) 84, ____, 110
b)
c)
24, ____, 57
Writing Explicit Equations
1. Determine that the sequence is
arithmetic.
2. Identify the common difference.
3. Create an explicit formula using
the first term in the sequence
and the common difference.
Write an explicit equation
for the sequence
3 , 7 , 11 , 15 , 19 , 23 , ...
Write an explicit equation for
the sequence
110 , 103 , 96 , 89 , 82 , 75 , …