Nth Term of Harmonic Progression Calculator

Search
Home	Math ↺
Math	Sequence and Series ↺
Sequence and Series	Harmonic Progression ↺

✖The First Term of HP is the value corresponding to the first term in the Harmonic Progression.ⓘ First term of HP [a]			+10% -10%
✖The Total Terms of HP is the total number of terms present in the given sequence of Harmonic Progression.ⓘ Total Terms of HP [n_Total]			+10% -10%
✖The Common Difference of HP is the difference of reciprocal of an arbitrary term from the reciprocal of its proceeding term of the Harmonic Progression.ⓘ Common Difference of HP [d]			+10% -10%

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

⎘ Copy

👎

Formula

✖

Nth Term of Harmonic Progression

Formula

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

Example

`"0.04"=1/("3"+("12"-1)*"2")`

Calculator

LaTeX

Reset

👍

Nth Term of Harmonic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Term of HP = 1/(First term of HP+(Total Terms of HP-1)*Common Difference of HP)
T_n = 1/(a+(n_Total-1)*d)
This formula uses 4 Variables

Variables Used

Nth Term of HP - The Nth Term of HP is the term corresponding to the index or position of the number n from the beginning in the given Harmonic Progression.
First term of HP - The First Term of HP is the value corresponding to the first term in the Harmonic Progression.
Total Terms of HP - The Total Terms of HP is the total number of terms present in the given sequence of Harmonic Progression.
Common Difference of HP - The Common Difference of HP is the difference of reciprocal of an arbitrary term from the reciprocal of its proceeding term of the Harmonic Progression.

STEP 1: Convert Input(s) to Base Unit

First term of HP: 3 --> No Conversion Required
Total Terms of HP: 12 --> No Conversion Required
Common Difference of HP: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = 1/(a+(n_Total-1)*d) --> 1/(3+(12-1)*2)

Evaluating ... ...

T_n = 0.04

STEP 3: Convert Result to Output's Unit

0.04 --> No Conversion Required

FINAL ANSWER

0.04 <-- Nth Term of HP

(Calculation completed in 00.000 seconds)

You are here -

Home » Math » Sequence and Series » Harmonic Progression » Nth Term of Harmonic Progression

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

Alithea Fernandes has verified this Calculator and 100+ more calculators!

< 2 Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression

Go Sum of First N Terms of HP = (1/Common Difference of HP)*ln((2*First term of HP+(2*Total Terms of HP-1)*Common Difference of HP)/(2*First term of HP-Common Difference of HP))

Nth Term of Harmonic Progression

Go Nth Term of HP = 1/(First term of HP+(Total Terms of HP-1)*Common Difference of HP)

Nth Term of Harmonic Progression Formula

Nth Term of HP = 1/(First term of HP+(Total Terms of HP-1)*Common Difference of HP)
T_n = 1/(a+(n_Total-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 HP = 1/(First term of HP+(Total Terms of HP-1)*Common Difference of HP) to calculate the Nth Term of HP, The Nth Term of Harmonic Progression formula is defined as the term corresponding to the index or position of the number n from the beginning in the given Harmonic Progression. Nth Term of HP 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 HP (a), Total Terms of HP (n_Total) & Common Difference of HP (d) and hit the calculate button. Here is how the Nth Term of Harmonic Progression calculation can be explained with given input values -> 0.04 = 1/(3+(12-1)*2).

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 of the number n from the beginning in the given Harmonic Progression and is represented as T_n = 1/(a+(n_Total-1)*d) or Nth Term of HP = 1/(First term of HP+(Total Terms of HP-1)*Common Difference of HP). The First Term of HP is the value corresponding to the first term in the Harmonic Progression, The Total Terms of HP is the total number of terms present in the given sequence of Harmonic Progression & The Common Difference of HP is the difference of reciprocal of an arbitrary term from the reciprocal of its proceeding term of the Harmonic Progression.

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 of the number n from the beginning in the given Harmonic Progression is calculated using Nth Term of HP = 1/(First term of HP+(Total Terms of HP-1)*Common Difference of HP). To calculate Nth Term of Harmonic Progression, you need First term of HP (a), Total Terms of HP (n_Total) & Common Difference of HP (d). With our tool, you need to enter the respective value for First term of HP, Total Terms of HP & Common Difference of HP and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Facebook
Twitter
WhatsApp
Reddit
LinkedIn
E-Mail

Let Others Know

✖

Facebook

Twitter

Copied!