Download Section 9.4 – Arithmetic Series

Name: ________________________ Date: ___________________ Period: ____________
Algebra 2: Section 9.4 Arithmetic Series Notes
Definition of a Series: The ______________ of the terms of a sequence: a1  a2  a3  ....an
Example 1)
Write each finite sequence as a finite series
a) 2, 3, 4, 5,
b) 16, 12, 8,
A series can be written with ________________________ notation where the sum of the
first n terms of a sequence is represented by
n
a
i 1
i
 a1  a2  a3  ....an
i is known as the index of the summation,
1 is the ________ limit and n is the ________ limit.
Example 2) Find each sum.
5
a)
 2i
i 1
 k
4
b)
3

1
k 2
Formula for the sum of a finite Arithmetic Series
The sum Sn of a finite arithmetic series can be found using the formula:
Where a1 is the first term, an is the nth term, and n is the number of terms.
Example 3) Find the sum of the even integers between 2 and 100.
Example 4) Find the sum of each. (Hint: the Formula!)
10
a)
100
  6  (n  1)3
b)
 ( 8  5k )
k 3
i 1
** Note: the number of terms in a series is equal to upper limit - lower limit + 1**
Example 5) A theater has 18 seats in the first row. Each successive row has three
additional seats. The theatre has 20 rows.
a) How many seats are in the 20th row?
b) What is the total seating capacity of the theatre?
Example 6) Given 3 + 12+ 21 + 30 + …… Find S25.
Example 7) Write each arithmetic series in summation notation.
a) 4 + 8 + 12 +16
b) 7 + 9 + 11 + ….. +21