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# Geometric progression

##### This calculator computes n-th term and sum of geometric progression
Timur2008-11-25 20:24:48
Geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio.

If module of common ratio is greater than 1 progression shows exponential growth of terms towards infinity, if it is less than 1, but not zero, progression shows exponential decay of terms towards zero.

N-th term of the progression is found as
$a_n=a_1q^{n-1}$

Partial sum to n
$S_n=\frac{a_nq-a_1}{q-1}=\frac{a_1-a_nq}{1-q}$
where q is not equal to 1

For q =1
$S_n=na_1$

The number of terms in infinite geometric progression will approach to infinity $n = \infty$. Sum of infinite geometric progression can only be defined if common ratio is at the range from -1 to 1 inclusive.

$S=\frac{a_1}{1-q}$
Geometric progression
N-th term:
Partial sum to n:
Infinite sum:

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