First Term 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 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 First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Harmonic Progression [a]

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Formula

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First Term of Harmonic Progression

Formula

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

Example

`"-19.983333"=1/"60"-(("6"-1)*"4")`

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First Term of Harmonic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
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.
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

Nth Term of Progression: 60 --> 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

a = 1/T_n-((n-1)*d) --> 1/60-((6-1)*4)

Evaluating ... ...

a = -19.9833333333333

STEP 3: Convert Result to Output's Unit

-19.9833333333333 --> No Conversion Required

FINAL ANSWER

-19.9833333333333 ≈ -19.983333 <-- First Term of Progression

(Calculation completed in 00.004 seconds)

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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)

< 5 Harmonic Progression Calculators

Sum of First N Terms of Harmonic 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)

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)

First Term of Harmonic Progression Formula

First Term of Progression = 1/Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)
a = 1/T_n-((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 First Term of Harmonic Progression?

First Term of Harmonic Progression calculator uses First Term of Progression = 1/Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression) to calculate the First Term of Progression, The First Term of Harmonic Progression formula is defined as the reciprocal of the first term of the given Harmonic Progression, which is the first term of the corresponding Arithmetic Progression. First Term of Progression is denoted by a symbol.

How to calculate First Term of Harmonic Progression using this online calculator? To use this online calculator for First Term of Harmonic Progression, enter Nth Term of Progression (T_n), Index N of Progression (n) & Common Difference of Progression (d) and hit the calculate button. Here is how the First Term of Harmonic Progression calculation can be explained with given input values -> -19.999273 = 1/60-((6-1)*4).

FAQ

What is First Term of Harmonic Progression?

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

How to calculate First Term of Harmonic Progression?

The First Term of Harmonic Progression formula is defined as the reciprocal of the first term of the given Harmonic Progression, which is the first term of the corresponding Arithmetic Progression is calculated using First Term of Progression = 1/Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression). To calculate First Term of Harmonic Progression, you need Nth Term of Progression (T_n), Index N of Progression (n) & Common Difference of Progression (d). With our tool, you need to enter the respective value for Nth 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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