GEOMETRIC PROGRESSION
Analysis
 
4. GENERAL OR NTH TERM OF A GEOMETRIC PROGRESSION

We can always find a formula which allows us to find any term in any geometric progression, as long as we know its position in the sequence. This formula is denoted as the general or nth term of the geometric progression.

6.- Examine the sequence in the window by going through the following steps::

step_1

Note that each term is the same as the preceding one multiplied by the common ratio.  (Check this by changing the value of n)
step_2

Note that each term can be expressed in terms of the first term.
(Change the value of n)

Note the relationship between the position of each term and the number the common ratio is raised to.
(Change the value of n)

Find the general term of the sequence in the example. Try different sequences and find a general formula for any sequence.
Step_3

Show the general term.

General or nth term

an= a1*r(n-1)
 
5. DETERMINING THE GENERAL OR NTH TERM OF A GEOMETRIC PROGRESSION

We are going to find the general or nth term of the following geometric progressions.

9.- Copy the following geometric progressions into your exercise book and work out the general term:

Terms a1 r an
1, 3, 9, 27, 81, ...      
-5, -10, -20, -40, ...      
1024, 512, 256, ...      
6, 6, 6, 6, ...      
100, 150, 225, ...      
1000, -100, 10, ...      

Write down the first term a1 and the common ratio r in each case, apply the general formula and carry out the operations indicated.

The results can be checked in the window.
       
           
  Juan Madrigal Muga
 
Spanish Ministry of Education. Year 2002
 
 

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