HOW TO DETERMINE IF THE GIVEN SEQUENCE IS GEOMETRIC SEQUENCE

A Geometric Progression is a sequence in which each term is obtained by multiplying a fixed non-zero number to the preceding term except the first term.

The fixed number is called common ratio. The common ratio is usually denoted by r.

To determine whether a sequence is geometric or not, we have to find the ratio between the first term and second term, second term and third term, third term and fourth term.

That is, 

t2/t1,  t3/t2 and t4/t3

If all the above ratios are equal, then the given sequence is geometric sequence.

Practice Problems

Problem 1 :

Check whether the following sequence is geometric or not.

3, 9, 27, 81, ..........

Solution :

First term (a)  =  3, common ratio

r  =  t2/t1

  =  9/3

r = 3

r  =  t3/t2

  =  27/9

r = 3

r  =  t2/t1

  =  81/27

r = 3

Because the  ratios are same, it is geometric sequence.

Problem 2 :

Check whether the following sequence is geometric or not.

4, 44, 444, 4444, ..........

Solution :

First term (a)  =  3, common ratio

r  =  t2/t1

  =  44/4

r = 11

r  =  t3/t2

  =  444/44

r = 111/11

r  =  t2/t1

  =  4444/444

r = 1111/111

Because the  ratios are same, it is geometric sequence.

Problem 3 :

Check whether the following sequence is geometric or not.

0.5, 0.05, 0.005, ..........

Solution :

First term (a)  =  0.5, common ratio

r  =  t2/t1

  =  0.05/0.5

r  =  0.1

r  =  t2/t1

  =  0.005/0.05

r = 0.1

Because the  ratios are same, it is geometric sequence.

Problem 4 :

Check whether the following sequence is geometric or not.

1/3, 1/6, 1/12, ..........

Solution :

First term (a)  =  1/3, common ratio

r  =  t2/t1

  =  (1/6)/(1/3)

r  =  1/2

r  =  t2/t1

  =  (1/12)/(1/6)

r = 1/2

Because the  ratios are same, it is geometric sequence.

Problem 5 :

Check whether the following sequence is geometric or not.

1, −5, 25, −125, ..........

Solution :

First term (a)  =  1/3, common ratio

r  =  t2/t1

  =  -5/1

r  =  -5

r  =  t2/t1

  =  25/(-5)

r = -5

Because the  ratios are same, it is geometric sequence.

Problem 6 :

Check whether the following sequence is geometric or not.

120, 60, 30, 18, ..........

Solution :

First term (a)  =  120, common ratio

r  =  t2/t1

  =  60/120

r  =  1/2

r  =  t2/t1

  =  30/60

r = 1/2

Because the  ratios are same, it is geometric sequence.

Problem 7 :

Check whether the following sequence is geometric or not.

16, 4, 1, 1/4, ..........

Solution :

First term (a)  =  16, common ratio

r  =  t2/t1

  =  4/16

r  =  1/4

r  =  t2/t1

 r  =  1/4

Because the ratios are same, it is geometric sequence.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Precalculus Problems and Solutions (Part - 15)

    May 24, 25 02:40 AM

    Precalculus Problems and Solutions (Part - 15)

    Read More

  2. Digital SAT Math Problems and Solutions (Part - 168)

    May 23, 25 07:42 PM

    Digital SAT Math Problems and Solutions (Part - 168)

    Read More

  3. Precalculus Problems and Solutions (Part - 14)

    May 23, 25 07:15 PM

    Precalculus Problems and Solutions (Part - 14)

    Read More