Sequences, Series and Summations 
 Section 8.2  
Sequence:  a function whose domain is the set of
natural numbers. natural numbers (counting numbers) {1, 2, 3, 4...} 
Series:  is a sum of a sequence. 
Write the first five terms of the sequence. a_{n} = 2n^{2 } n 
Solve 
Step 

a_{1} = 2(1)^{2 } 1 = 2(1)  1 = 2  1 = 1 
Start with n = 1  
a_{2} = 2(2)^{2 } 2 = 2(4)  2 = 8  2 = 6  n = 2  
a_{3} = 2(3)^{2 } 3 = 2(9)  3 = 18  3 = 15  n = 3  
a_{4} = 2(4)^{2 } 4 = 2(16)  4 = 32  4 = 28  n = 4  
a_{5} = 2(5)^{2 } 5 = 2(25)  5 = 50  5 = 45  n = 5  
The first five terms are 1, 6, 15, 28, 45 

a_{n} = 2n^{2 } n can also be written as f(n) = 2n^{2 } n . The term a_{n} indicates it is a special function called a sequence. 
Write the first five terms of the sequence. a_{n} = n^{2 }+ 3n 
[Solution] 


Evaluate the sum. 
We add the first five terms of the sequence a_{n} = 2n^{2 } n from example 1.  
Solve 
Step 

The first five terms are 1, 6, 15, 28, 45  

= 1 + 6 + 15 + 28 + 45 = 95  n
= 1 means start at 1 5 means end at 5. 

Evaluate the sum. 
[Solution] 


Evaluate the sum. 
Solve 
Step 

K
= 3 means
start
at 3 5 means end at 5. k = 3, 4, 5 

Add the fractions  
The sum of a sequence is called a series.  
Evaluate the sum. 
[Solution] 


Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada