AA
11-2 Arithmetic Series
Series:
* An indicated sum of the terms of a
sequence.
Arithmetic Series:
* The sum of the arithmetic sequence.
Arithmetic Sequence
-9, -3, 3
3 8 13 , 18
, ,
8 8 8
8
Arithmetic Series
-9 + -3 + 3
3 8 13 18
+ + +
8 8 8
8
1. Find the sum of the first 20 even numbers,
beginning with 2.
Sum of an Arithmetic Series:
* The sum Sn of the first n terms of an
arithmetic series is given by:
n
Sn = 2 [ 2a1 + (n - 1)d]
or
n
Sn = (a1 + an)
2
2.
A radio station is giving away $124,000 during
September. They want to increase the amount they
give away each day by $100, how much should they
give away on the first day?
3. Find the first four terms of an arithmetic
series in which a1 = 14, an = 29, and
Sn = 129.
Sigma Notation:
* An alternate way of writing out a series.
* Symbol: ∑
3 + 6 + 9 + 12 + ...+ 30 written in sigma
notation:
last value
of n
10
∑ 3n
n=1
formula for the
terms of the
series.
first value
of n
read as "the sum of 3n as n goes from
1 to 10"
Index of Summation:
* The variable that is used in the index.
10
4. Evaluate ∑ (2k + 1)
k=3
11 - 2 Arithmetic Series
pg. 586 - 587
#1, 3, 14 - 16, 20 - 22, 27, 28, 30,
31, 34, 35, 41, 42, 45, 49, 50, 54,
60 - 62, 63, 64
(25 problems)