Geometric progression is the progression in which every next term is found by multiplying the previous term by a fixed number. In other words, we can say that it is the progression in which any term divided by previous term always remain constant. Lets take an example of geometric progression.
2, 4 , 8, 16, 32, 64, ….
Is it a geometric progression? Yes. Lets choose any number from the progression. For example if we choose 16. Divide 16 by the previous term which is 8 and we get 2 as a result. Now try to choose another term. For example if we choose 8. Divide 8 by previous term which is 4 and we get 2 as a result. Similarly in this progression, any term divided by previous term will always remain constant. This constant number is called common ratio in geometric progressions. Note that first term of geometric progression is also represented by small letter a. Common ratio is represented by small letter r.
Now you should be able to tell if the given progression is geometric or not?
Is this a geometric progression? 3, 9, 27, 81 ….
Yes, because you get next term by multiplying previous term by a fixed number which is 3. In other words, any term divided by previous term is equal to 3 in this case.
Is this geometric progress? 1, -3, 9, -27, 81 …..
Yes, because you get next term by multiplying previous term by a fixed number which is -3. In other words, any term divided by previous term is equal to -3 in this case.
Is this geometric progression? 3, 6, 9, 12, 15 …..
No, because any term divided by previous term is not fixed in this case.
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