A geometric progression is a sequence of numbers in which each successive number is obtained by multiplying a fixed quantity with the previous number.

The fixed or constant quantity that is multiplied to get the next term in a geometric progression is known as the

Let each term from the beginning in a geometric progression be represented by the following:

In the above sequence, the second term (a

Thus, if in a geometric progression,

Thus a geometric progression with first term

The fixed or constant quantity that is multiplied to get the next term in a geometric progression is known as the

**common ratio**. It is commonly represented by the letter*r*.Let each term from the beginning in a geometric progression be represented by the following:

a(where a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, ...

_{1}is the first term, a_{2}the second term, and so on.)In the above sequence, the second term (a

_{2}) is obtained by multiplying a fixed quantity, the common ratio, to the first term (a_{1}). That is, if the common ratio is*r*,aSimilarly the third term (a_{2}= a_{1}x r

_{3}) is obtained by multiplying a fixed quantity (the common ratio) to the second term (a_{2}). That is, if the common ratio is*r*,aThus the common ratio (_{3}= a_{2}x r

*r*) of a geometric progression can be obtained by dividing its any term by the previous term. Thus, in the following geometric progression:2, 4, 8, 16, ...the common ratio is 4/2 = 2. Similarly the common ratios of the following geometric progressions are given:

- 3, 9, 27, ... (common ratio,
*r*= 3) - 2, 6, 18, ... (common ratio,
*r*= 2) - 1/2, 1/4, 1/8, 1/16, ... (common ratio,
*r*= 1/2)

Thus, if in a geometric progression,

*a*is the first term and*r*is the common ratio, then- Second term = a x r = ar
- third term = (second term) x r = ar
^{2} - fourth term = (third term) x r = ar
^{3} - and so on..

Thus a geometric progression with first term

*a*and common ratio*r*can be represented byar, arRelated posts:^{2}, ar^{3}, ar^{4}, ...

- Sum of 'n' terms of a geometric progression
- Sum of an infinite geometric progression
- Progressions in general

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