jdlogo

jdlogo

jdlogo

jdlogo

jdlogo

Home

Arithmetic Sequences

Geometric Sequences

Arithmetic Series

Geometric Series

Sigma Notation

Mathematical Induction

Review&Test

 

jdsmathnotes

 


 UNIT 10 : SEQUENCES AND SERIES

 LESSON 3: ARITHMETIC SERIES

 

 

Arithmetic Series:

Recall a sequence such as 2, 3, 8, 13, is called an Arithmetic Sequence. These sequences have the following properties.

        Terms are denoted as t1 , t2 , t3 , referring to term1, term 2, term 3

        The difference between successive terms is constant. ie t2 t1 = t3 t2 = t4 t3 etc

        This difference is called the common difference and denoted using the letter d. Here d = 5.

        The first term is denoted using the letter a. Here a = -2.

        Successive terms are found by adding the common difference, d, to the preceding term. Hence t5 = 13 + 5 = 18 etc.

        The formula for the general term or nth term is tn = a + (n 1)d

 

Text Box: a = t1 = first term
d = common difference
n = term number
tn = nth term or general term
 

 

 

 

 

 


Definition: The sum of the terms of an arithmetic sequence is an Arithmetic Series.

Text Box:

Text Box: n = the number of terms
t1 = a = the first term
tn = l = the last term
d = the common difference
Sn = the sum of the series
 

 

 

 

 

 

 

 


Example 1: Given the first few terms.

For the arithmetic series below, above, find t11, the general term tn and the sum of 40 terms S40.

Solution:

a = 1

d = 3

n = 11

tn = ?

S40 = ?

 

 

Example 2: Given the first and last terms.

a = - 3

d = - 4

tn = - 219

n = ?

Sn = ?

 
Solution:

 

Example 3: Given two terms.

The fourth and seventh terms of an arithmetic series are 8 and 17 respectively. Find a, d and S26.

Solution:

 

 

 

Return to top of page

Click here to go to homework questions