Geometric Progression Formulas
In mathematics, a geometric progression (also inaccurately known as a geometric series) is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.
a geometric sequence can be written as:
Formulae for the nth term can be defined as:
a_{n} = a_{1}.q^{n1}
The common ratio then is:
q = 

A sequence with a common ratio of 2 and a scale factor of 1 is
1, 2, 4, 8, 16, 32...
A sequence with a common ratio of 1 and a scale factor of 5 is
5, 5, 5, 5, 5, 5,...
If the common ratio is:
 Negative, the results will alternate between positive and negative.
 Greater than 1, there will be exponential growth towards infinity (positive).
 Less than 1, there will be exponential growth towards infinity (positive and negative).
 Between 1 and 1, there will be exponential decay towards zero.
 Zero, the results will remain at zero
Geometric Progression Properties
a_{1}.a_{n} = a_{2}.a_{n1} =...= a_{k}.a_{nk+1}
Formula for the sum of the first n numbers of a geometric series
S_{n} =  a_{1}  a_{n}q 1  q  = a_{1}.  1  q^{n} 1  q 
Infinite geometric series where q < 1
If q < 1 then a_{n} > 0,
when n > ∞.
The sum S of such an infinite geometric series is given by the formula:
S =  a_{1} 

Geometric Progression Calculator
Geometric Progression Problems
Problem 1.
Is the sequence 2, 4, 6, 8... a geometric progression?
Solution: No, it is not. (2, 4, 8 is a geometric progression)
Problem 2
If 2, 4, 8... form a geometric progression. What is the 10th term?
Solution: We can use the formula a_{n} = a_{1} . q^{n1}
a_{10} = 2 . 2^{101} = 2 . 512 = 1024
Problem 3
Find the scale factor and the command ratio of a geometric progression if
a_{5}  a_{1} = 15
a_{4}  a_{2} = 6
Solution: there are two geometric progressions. The first one has a
scale factor 1 and common ratio = 2
the second decidion is 16, 1/2
Additional problems:
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