Skip Navigation Links
   
Determine whether a Sequence is an AP or not
To enroll in any of our courses, click here
 
   
Determine whether a Sequence is an A.P. or not
Arithmetic Progression: An arithmetic progression or arithmetic sequence, is a sequence of numbers such that the differences between two successive terms is always a constant .
For example, the sequence 1,5, 9, 13, 17, 21... is an arithmetic progression with common difference 4.

ALGORITHM
STEP I Obtain an
STEP II Replace n by (n + l) in an to get an + 1
STEP III Calculate an + 1- an
STEP IV Check the value of an+ 1- an. lf an+ 1- an is independent of n, then the given sequence is an A.P. Otherwise it is not an A.P. Following examples will illustrate the above algorithm.
People who saw this lesson also found the
following lessons useful:
Quadratic Equations: Miscellaneous Problem
Internal and External bisector of an Angle of a Triangle
Converse of Basic Proportionality Theorem
Cyclic Quadrilateral Theorem
Mensuration Miscellaneous Example
Example 1: Show that the sequence defined by an = 4n + 5 is an A.P. Also, find its common difference.
Solution: you have,
         an = 4n + 5.
Replacing n by (n + 1), we get
         an + 1 = 4(n + 1) + 5 = 4n + 9
Now, an + 1 - an = (4n + 9) - (4n + 5) = 4
Clearly, an + 1 - an is independent of n and is equal to 4. So, the given sequence is an A.P. with common difference 4.

Example 2: The nth term of a sequence is 3n - 2. Is the sequence an A.P. ? If so, find its 10th term.
Solution: you have an = 3n - 2. Clearly an is a linear expression in n. So, the given sequence is an A.P. with common difference 3.
Putting n = 10,
you get a10 = 3 * 10 - 2 = 28.
so the 10th term will be 28.
 
   
As many of you know, Winpossible's online courses use a unique teaching method where an instructor explains the concepts in any given area to you in his/her own voice and handwriting, just like you see your teacher explain things to you on a blackboard in your classroom. All our courses include teacher's instruction, practice questions as well as end-of-lesson quizzes for practice. You can enroll in any of our online courses by clicking here.

The format of Winpossible's online courses is also very suitable for teachers who are using an interactive whiteboard such as Smartboard on Promethean in their classrooms, because the course lessons can be easily displayed on such interactive whiteboards. Volume pricing is available for schools interested in our online courses. For more information, please contact us at educators@winpossible.com.

 
       
     
 Copyright © Winpossible, 2010 - 2011
Best viewed in 1024x768 & IE 5.0 or later version