Number of Terms of Geometric Progression Calculator

✖The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.ⓘ Common Ratio of Progression [r]			+10% -10%
✖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.ⓘ Number of Terms of Geometric Progression [n]

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Formula

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Number of Terms of Geometric Progression

Formula

`"n" = log("r","T"_{"n"}/"a")+1`

Example

`"5.321928"=log("2","60"/"3")+1`

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Number of Terms of Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Index N of Progression = log(Common Ratio of Progression,Nth Term of Progression/First Term of Progression)+1
n = log(r,T_n/a)+1
This formula uses 1 Functions, 4 Variables

Functions Used

log - Logarithmic function is an inverse function to exponentiation., log(Base, Number)

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Common Ratio of Progression: 2 --> No Conversion Required
Nth Term of Progression: 60 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = log(r,T_n/a)+1 --> log(2,60/3)+1

Evaluating ... ...

n = 5.32192809488736

STEP 3: Convert Result to Output's Unit

5.32192809488736 --> No Conversion Required

FINAL ANSWER

5.32192809488736 ≈ 5.321928 <-- Index N of Progression

(Calculation completed in 00.004 seconds)

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< 2 Number of Terms in Geometric Progression Calculators

Number of Total Terms of Geometric Progression

Go Number of Total Terms of Progression = log(Common Ratio of Progression,Last Term of Progression/First Term of Progression)+1

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

< 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

Number of Terms of Geometric Progression Formula

Index N of Progression = log(Common Ratio of Progression,Nth Term of Progression/First Term of Progression)+1
n = log(r,T_n/a)+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 Number of Terms of Geometric Progression?

Number of Terms of Geometric Progression calculator uses Index N of Progression = log(Common Ratio of Progression,Nth Term of Progression/First Term of Progression)+1 to calculate the Index N of Progression, The Number of Terms of Geometric Progression formula is defined as the value of n for the nth term or the position of the nth term in a Geometric Progression. Index N of Progression is denoted by n symbol.

How to calculate Number of Terms of Geometric Progression using this online calculator? To use this online calculator for Number of Terms of Geometric Progression, enter Common Ratio of Progression (r), Nth Term of Progression (T_n) & First Term of Progression (a) and hit the calculate button. Here is how the Number of Terms of Geometric Progression calculation can be explained with given input values -> 9.840253 = log(2,60/3)+1.

FAQ

What is Number of Terms of Geometric Progression?

The Number of Terms of Geometric Progression formula is defined as the value of n for the nth term or the position of the nth term in a Geometric Progression and is represented as n = log(r,T_n/a)+1 or Index N of Progression = log(Common Ratio of Progression,Nth Term of Progression/First Term of Progression)+1. The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression, 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.

How to calculate Number of Terms of Geometric Progression?

The Number of Terms of Geometric Progression formula is defined as the value of n for the nth term or the position of the nth term in a Geometric Progression is calculated using Index N of Progression = log(Common Ratio of Progression,Nth Term of Progression/First Term of Progression)+1. To calculate Number of Terms of Geometric Progression, you need Common Ratio of Progression (r), Nth Term of Progression (T_n) & First Term of Progression (a). With our tool, you need to enter the respective value for Common Ratio of Progression, Nth Term of Progression & First Term of Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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