Algebra 2: Section 11-2 Arithmetic Sequences
Standard: Students find the general term of arithmetic series.
Arithmetic Sequence Formulas
Recursive Formula
Explicit Formula
an  a1  (n  1)d
a1  a given value
an  an 1  d
In these formulas, a n is the nth term, a1 is the first term,
n is the number of the term, and d is the common difference.
 In an arithmetic sequence: the difference between consecutive terms is
constant.
 A common difference is: can be positive (terms are increasing in value)
or negative (terms are decreasing in value).
 The arithmetic mean of any two numbers is: the average of the two
numbers.
Example 1) Identifying an Arithmetic Sequence
Is the sequence arithmetic?
a) 7, 10, 13, 16, …
The common difference is _____. This _____ an arithmetic sequence.
b) the sequence of dots shown below
3,
6,
10,
15
There is no common difference. This _________ an arithmetic sequence.
Example 2) Saving Money
a) Suppose you have already save $75 toward the purchase of a new CD
player. You plan to save at least $12 a week from money you earn at a parttime job. In all, what is the minimum amount you will have saved after 26
weeks?
Find the 27th term of the sequence 75, 87, 99, …
an  a1  (n  1)d
Why was it necessary to find the value if the 27th term, not the 26th term?
Example 3) Using the Arithmetic Mean
Find the missing term of the arithmetic sequence
50, ____, 92
Arithmetic mean

+
The missing term is ____.
Quick Check
Ex. 1) Is the given sequence arithmetic? If so, identify the common
difference.
a) 2, 5, 7, 12, …
b) 48, 45, 42, 39, …
Ex. 2)
b) Use the explicit formula to find the 25th term in the sequence
5, 11, 17, 23, 29, …
Ex. 3)
a) Find the missing term of the arithmetic sequence 24, __, 57.
b) Write an expression that shows the arithmetic mean of a6 and a7 .
Assignment page 618 #1-29 odds
Day 2
Ex. 4) Extra Examples.
You are given two terms of each arithmetic sequence, find a1 and d.
a) a4  8 and a7  20
b) In an arithmetic sequence with a1  2 and d  2 , which term is -82?
Ex. 5) Extra Example
Write an explicit and a recursive formula for the sequence.
-2, 5, 12, 19, 26, 33, …
Assignment page 619 #47-59 odds, 75, 77, 90-93 all