Common Ratio of Geometric Progression Calculator

✖The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.ⓘ Nth Term of Progression [T_n]			+10% -10%
✖The (N-1)th Term of Progression is the term corresponding to the index or position (n-1) from the beginning of the given Progression.ⓘ (N-1)th Term of Progression [T_n-1]			+10% -10%

✖The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.ⓘ Common Ratio of Geometric Progression [r]

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Formula

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Common Ratio of Geometric Progression

Formula

`"r" = "T"_{"n"}/"T"_{"n-1"}`

Example

`"1.2"="60"/"50"`

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Common Ratio of Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression
r = T_n/T_n-1
This formula uses 3 Variables

Variables Used

Common Ratio of Progression - The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.
Nth Term of Progression - The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.
(N-1)th Term of Progression - The (N-1)th Term of Progression is the term corresponding to the index or position (n-1) from the beginning of the given Progression.

STEP 1: Convert Input(s) to Base Unit

Nth Term of Progression: 60 --> No Conversion Required
(N-1)th Term of Progression: 50 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = T_n/T_n-1 --> 60/50

Evaluating ... ...

r = 1.2

STEP 3: Convert Result to Output's Unit

1.2 --> No Conversion Required

FINAL ANSWER

1.2 <-- Common Ratio of Progression

(Calculation completed in 00.004 seconds)

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Created by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has created this Calculator and 25+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 1100+ more calculators!

< 3 Common Ratio of Geometric Progression Calculators

Common Ratio of Geometric Progression given Last Term

Go Common Ratio of Progression = (Last Term of Progression/First Term of Progression)^(1/(Number of Total Terms of Progression-1))

Common Ratio of Geometric Progression given Nth Term

Go Common Ratio of Progression = (Nth Term of Progression/First Term of Progression)^(1/(Index N of Progression-1))

Common Ratio of Geometric Progression

Go Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression

< 9 Geometric Progression Calculators

Sum of Total Terms of Geometric Progression

Go Sum of Total Terms of Progression = (First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression)-1))/(Common Ratio of Progression-1)

Sum of Last N Terms of Geometric Progression

Go Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1)

Sum of First N Terms of Geometric Progression

Go Sum of First N Terms of Progression = (First Term of Progression*(Common Ratio of Progression^Index N of Progression-1))/(Common Ratio of Progression-1)

Nth Term from End of Geometric Progression

Go Nth Term from End of Progression = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression))

Number of Terms of Geometric Progression

Go Index N of Progression = log(Common Ratio of Progression,Nth Term of Progression/First Term of Progression)+1

First Term of Geometric Progression

Go First Term of Progression = Nth Term of Progression/(Common Ratio of Progression^(Index N of Progression-1))

Nth Term of Geometric Progression

Go Nth Term of Progression = First Term of Progression*(Common Ratio of Progression^(Index N of Progression-1))

Sum of Infinite Geometric Progression

Go Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression)

Common Ratio of Geometric Progression

Go Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression

Common Ratio of Geometric Progression Formula

Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression
r = T_n/T_n-1

What is a Geometric Progression?

In Mathematics a Geometric Progression or simply GP also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed real number called the common ratio. For example, the sequence 2, 6, 18, 54,... is a Geometric Progression with common ratio 3. If the sum of all terms in the progression is a finite number or if the infinite sum of the progression exists then the we say it is an Infinite Geometric Progression or Infinite GP. And if the infinite sum of the progression does not exist, then it is a Finite Geometric Progression or Finite GP. If the absolute value of the common ratio is greater than 1 then the GP will be a Finite GP and if it is less than 1 then the GP will be an Infinite GP.

How to Calculate Common Ratio of Geometric Progression?

Common Ratio of Geometric Progression calculator uses Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression to calculate the Common Ratio of Progression, The Common Ratio of Geometric Progression formula is defined as the ratio of any term in the Geometric Progression to its preceding term. Common Ratio of Progression is denoted by r symbol.

How to calculate Common Ratio of Geometric Progression using this online calculator? To use this online calculator for Common Ratio of Geometric Progression, enter Nth Term of Progression (T_n) & (N-1)th Term of Progression (T_n-1) and hit the calculate button. Here is how the Common Ratio of Geometric Progression calculation can be explained with given input values -> 27.5 = 60/50.

FAQ

What is Common Ratio of Geometric Progression?

The Common Ratio of Geometric Progression formula is defined as the ratio of any term in the Geometric Progression to its preceding term and is represented as r = T_n/T_n-1 or Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression. The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression & The (N-1)th Term of Progression is the term corresponding to the index or position (n-1) from the beginning of the given Progression.

How to calculate Common Ratio of Geometric Progression?

The Common Ratio of Geometric Progression formula is defined as the ratio of any term in the Geometric Progression to its preceding term is calculated using Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression. To calculate Common Ratio of Geometric Progression, you need Nth Term of Progression (T_n) & (N-1)th Term of Progression (T_n-1). With our tool, you need to enter the respective value for Nth Term of Progression & (N-1)th Term of Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Common Ratio of Progression?

In this formula, Common Ratio of Progression uses Nth Term of Progression & (N-1)th Term of Progression. We can use 2 other way(s) to calculate the same, which is/are as follows -

Common Ratio of Progression = (Nth Term of Progression/First Term of Progression)^(1/(Index N of Progression-1))
Common Ratio of Progression = (Last Term of Progression/First Term of Progression)^(1/(Number of Total Terms of Progression-1))

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