# Geometric progression. The common ratio and the first term

Finding the common ratio and the first term the geometric progression for two adjacent terms.

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#### khajit_94

Created: 2015-11-01 20:03:51, Last updated: 2020-11-03 14:19:32

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The site already has a calculator for the geometric progression - Geometric progression, which allows you to find the sum of its terms. However, there is also another task - for two adjacent terms of geometric progression find common ratio and its first term. It is clear that in such formulation of the problem we are talking about increasing geometric progression, the first member of which, as well as the common ratio, are integers.

Common ratio and two adjacent terms of geometric progression are related like this

$a_n=a_{n-1}q$,

hence

$q=\frac{a_n}{a_{n-1}}$

To get the first term, we should devide every previous one by common ratio, until we reach last possible integer value.
Last integer will be the first term of a geometric progression. Actually, I've made calculator below so you won't get tired with all this divisions.

#### Geometric progression. The denominator and the first term

First term of a geometric progression

Denominator of a geometric progression

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PLANETCALC, Geometric progression. The common ratio and the first term