Number of Terms of Harmonic 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 First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%
✖The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.ⓘ Common Difference of Progression [d]			+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 Harmonic Progression [n]

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Formula

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Number of Terms of Harmonic Progression

Formula

`"n" = ((1/"T"_{"n"}-"a")/"d")+1`

Example

`"0.254167"=((1/"60"-"3")/"4")+1`

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Number of Terms of Harmonic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1
n = ((1/T_n-a)/d)+1
This formula uses 4 Variables

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.
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.
Common Difference of Progression - The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

STEP 1: Convert Input(s) to Base Unit

Nth Term of Progression: 60 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = ((1/T_n-a)/d)+1 --> ((1/60-3)/4)+1

Evaluating ... ...

n = 0.254166666666667

STEP 3: Convert Result to Output's Unit

0.254166666666667 --> No Conversion Required

FINAL ANSWER

0.254166666666667 ≈ 0.254167 <-- Index N of Progression

(Calculation completed in 00.005 seconds)

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Home » Math » Sequence and Series » AP,GP and HP » Harmonic Progression » Number of Terms of Harmonic Progression

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< 6 Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression

Go Sum of First N Terms of Progression = (1/Common Difference of Progression)*ln((2*First Term of Progression+(2*Index N of Progression-1)*Common Difference of Progression)/(2*First Term of Progression-Common Difference of Progression))

Number of Terms of Harmonic Progression

Go Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1

First Term of Harmonic Progression

Go First Term of Progression = 1/Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)

Nth Term of Harmonic Progression

Go Nth Term of Progression = 1/(First Term of Progression+(Index N of Progression-1)*Common Difference of Progression)

Nth Term of Harmonic Progression from End

Go Nth Term of Progression = 1/(Last Term of Progression-(Index N of Progression-1)*Common Difference of Progression)

Common Difference of Harmonic Progression

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

Number of Terms of Harmonic Progression Formula

Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1
n = ((1/T_n-a)/d)+1

What is Harmonic Progression ?

In Mathematics, a Harmonic Progression is a progression formed by taking the reciprocals of an arithmetic progression. Equivalently, a sequence is a Harmonic Progression when each term is the harmonic mean of the neighboring terms.

How to Calculate Number of Terms of Harmonic Progression?

Number of Terms of Harmonic Progression calculator uses Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1 to calculate the Index N of Progression, The Number of Terms of Harmonic Progression formula is defined as the total number of terms present in the given sequence of Harmonic Progression. Index N of Progression is denoted by n symbol.

How to calculate Number of Terms of Harmonic Progression using this online calculator? To use this online calculator for Number of Terms of Harmonic Progression, enter Nth Term of Progression (T_n), First Term of Progression (a) & Common Difference of Progression (d) and hit the calculate button. Here is how the Number of Terms of Harmonic Progression calculation can be explained with given input values -> 0.250182 = ((1/60-3)/4)+1.

FAQ

What is Number of Terms of Harmonic Progression?

The Number of Terms of Harmonic Progression formula is defined as the total number of terms present in the given sequence of Harmonic Progression and is represented as n = ((1/T_n-a)/d)+1 or Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference 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 Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

How to calculate Number of Terms of Harmonic Progression?

The Number of Terms of Harmonic Progression formula is defined as the total number of terms present in the given sequence of Harmonic Progression is calculated using Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1. To calculate Number of Terms of Harmonic Progression, you need Nth Term of Progression (T_n), First Term of Progression (a) & Common Difference of Progression (d). With our tool, you need to enter the respective value for Nth Term of Progression, First Term of Progression & Common Difference 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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