Common Ratio of Geometric Progression given Nth Term 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 First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%
✖The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.ⓘ Index N of Progression [n]			+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 given Nth Term [r]

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Formula

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Common Ratio of Geometric Progression given Nth Term

Formula

`"r" = ("T"_{"n"}/"a")^(1/("n"-1))`

Example

`"1.820564"=("60"/"3")^(1/("6"-1))`

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Common Ratio of Geometric Progression given Nth Term Solution

STEP 0: Pre-Calculation Summary

Formula Used

Common Ratio of Progression = (Nth Term of Progression/First Term of Progression)^(1/(Index N of Progression-1))
r = (T_n/a)^(1/(n-1))
This formula uses 4 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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
Index N of Progression - The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

STEP 1: Convert Input(s) to Base Unit

Nth Term of Progression: 60 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = (T_n/a)^(1/(n-1)) --> (60/3)^(1/(6-1))

Evaluating ... ...

r = 1.82056420302608

STEP 3: Convert Result to Output's Unit

1.82056420302608 --> No Conversion Required

FINAL ANSWER

1.82056420302608 ≈ 1.820564 <-- Common Ratio of Progression

(Calculation completed in 00.004 seconds)

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< 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

Common Ratio of Geometric Progression given Nth Term Formula

Common Ratio of Progression = (Nth Term of Progression/First Term of Progression)^(1/(Index N of Progression-1))
r = (T_n/a)^(1/(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 given Nth Term?

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

How to calculate Common Ratio of Geometric Progression given Nth Term using this online calculator? To use this online calculator for Common Ratio of Geometric Progression given Nth Term, enter Nth Term of Progression (T_n), First Term of Progression (a) & Index N of Progression (n) and hit the calculate button. Here is how the Common Ratio of Geometric Progression given Nth Term calculation can be explained with given input values -> 3.405934 = (60/3)^(1/(6-1)).

FAQ

What is Common Ratio of Geometric Progression given Nth Term?

The Common Ratio of Geometric Progression given Nth Term formula is defined as the ratio of any term in the Geometric Progression to its preceding term and calculated using the nth term of Geometric Progression and is represented as r = (T_n/a)^(1/(n-1)) or Common Ratio of Progression = (Nth Term of Progression/First Term of Progression)^(1/(Index N of Progression-1)). The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression, The First Term of Progression is the term at which the given Progression starts & The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

How to calculate Common Ratio of Geometric Progression given Nth Term?

The Common Ratio of Geometric Progression given Nth Term formula is defined as the ratio of any term in the Geometric Progression to its preceding term and calculated using the nth term of Geometric Progression is calculated using Common Ratio of Progression = (Nth Term of Progression/First Term of Progression)^(1/(Index N of Progression-1)). To calculate Common Ratio of Geometric Progression given Nth Term, you need Nth Term of Progression (T_n), First Term of Progression (a) & Index N of Progression (n). With our tool, you need to enter the respective value for Nth Term of Progression, First Term of Progression & Index N 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, First Term of Progression & Index N 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/(N-1)th Term of Progression
Common Ratio of Progression = (Last Term of Progression/First Term of Progression)^(1/(Number of Total Terms of Progression-1))

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