Download Section 9.2 – Arithmetic Sequences

Name: ________________________ Date: ___________________ Period: ____________
Algebra 2: Section 9.2 Arithmetic Sequences Notes
Definition of an Arithmetic Sequence
An arithmetic sequence is a sequence in which each term after the first differs from the preceding term
by a _____________ amount.
The difference between consecutive terms is called the ___________________________ of the sequence.
An arithmetic sequence is a _____________________________ with a ____________________ domain.
Example 1: Is the following sequence an arithmetic sequence?
a)
51, 39, 27, 15, ...
b)
16, 8, 4, 2, ...
Two Formulas of finding the nth term.
Recursive Formula – uses the previous term
to find the next one.
Explicit Formula – gives the nth term
without reference to any previous term.
Only uses the first term.
Recursive Formula for the General Term
( an ) of an Arithmetic Sequence:
Explicit Formula for the General Term
( an ) of an Arithmetic Sequence:
Example:
Example:
15, 25, 35, 45, …..
Example 2:
Given
Find
15, 25, 35, 45, …..
a1 = 3
an = an-1 + 4
a2 =
a3 =
a4 =
Example 3: What is the 100th term of the arithmetic sequence that begins 6,11,…?
Example 4: What are the second and third terms of the arithmetic sequence 100, ____, ____, 82,…?
Example 5: An arithmetic mean is the average of two numbers. What is the arithmetic mean
between 15 and 59?
Try It!!
a) What is the 46th term of the arithmetic sequence that begins 3,5,7,…?
b) What are the three arithmetic means between 7 and 15?
c) Given b1 = -2
bn = bn-1 - 3
Find the first 5 terms of the sequence.
d) The number of seats in the first 13 rows in a section of an arena form an arithmetic sequence.
Rows 1 and 2 are show in the picture below. How many seats are in row 13?