LCM of three numbers

Nth Term of Harmonic Progression Calculator

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✖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 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 Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.ⓘ Nth Term of Harmonic Progression [T_n]

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Nth Term of Harmonic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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

First Term of Progression: 3 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = 1/(a+(n-1)*d) --> 1/(3+(6-1)*4)

Evaluating ... ...

T_n = 0.0434782608695652

STEP 3: Convert Result to Output's Unit

0.0434782608695652 --> No Conversion Required

FINAL ANSWER

0.0434782608695652 ≈ 0.043478 <-- Nth Term of Progression

(Calculation completed in 00.004 seconds)

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Created by Mayank Tayal

National Institute of Technology (NIT), Durgapur

Mayank Tayal has created this Calculator and 25+ more calculators!

Verified by Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

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< Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression

LaTeX 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

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

Nth Term of Harmonic Progression

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

Common Difference of Harmonic Progression

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

< Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression

First Term of Harmonic Progression

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

Nth Term of Harmonic Progression

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

Common Difference of Harmonic Progression

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

Nth Term of Harmonic Progression Formula

LaTeX Go

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

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 Nth Term of Harmonic Progression?

Nth Term of Harmonic Progression calculator uses Nth Term of Progression = 1/(First Term of Progression+(Index N of Progression-1)*Common Difference of Progression) to calculate the Nth Term of Progression, The Nth Term of Harmonic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Harmonic Progression. Nth Term of Progression is denoted by T_n symbol.

How to calculate Nth Term of Harmonic Progression using this online calculator? To use this online calculator for Nth Term of Harmonic Progression, enter First Term of Progression (a), Index N of Progression (n) & Common Difference of Progression (d) and hit the calculate button. Here is how the Nth Term of Harmonic Progression calculation can be explained with given input values -> 0.043478 = 1/(3+(6-1)*4).

FAQ

What is Nth Term of Harmonic Progression?

The Nth Term of Harmonic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Harmonic Progression and is represented as T_n = 1/(a+(n-1)*d) or Nth Term of Progression = 1/(First Term of Progression+(Index N of Progression-1)*Common Difference of 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 & The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

How to calculate Nth Term of Harmonic Progression?

The Nth Term of Harmonic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Harmonic Progression is calculated using Nth Term of Progression = 1/(First Term of Progression+(Index N of Progression-1)*Common Difference of Progression). To calculate Nth Term of Harmonic Progression, you need First Term of Progression (a), Index N of Progression (n) & Common Difference of Progression (d). With our tool, you need to enter the respective value for First Term of Progression, Index N 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.

How many ways are there to calculate Nth Term of Progression?

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

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

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