# Geometric progression

This calculator computes n-th term and sum of geometric progression

### This page exists due to the efforts of the following people:

#### Michele

Created: 2011-07-16 04:17:35, Last updated: 2020-12-11 12:26:32

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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 the common ratio module is greater than 1, progression shows the 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 $n = \infty$. The sum of infinite geometric progression can only be defined if the common ratio ranges from -1 to 1 inclusive.

$S=\frac{a_1}{1-q}$

#### Geometric progression

Digits after the decimal point: 2
N-th term

Partial sum to n

Infinite sum

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PLANETCALC, Geometric progression