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)
Tn = 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
Tn = 1/(a+(n-1)*d) --> 1/(3+(6-1)*4)
Evaluating ... ...
Tn = 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)

Credits

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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5 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)
Common Difference of Harmonic Progression
Go Common Difference of Progression = (1/Nth Term of Progression-1/(N-1)th Term of Progression)

4 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))
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)
Common Difference of Harmonic Progression
Go Common Difference of Progression = (1/Nth Term of Progression-1/(N-1)th Term of Progression)

Nth Term of Harmonic Progression Formula

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