The formula to find the${n^{th}}$term of harmonic progression is.
$
{\text{a}}{\text{. }}\dfrac{1}{{a - \left( {n - 1} \right)d}} \\
{\text{b}}{\text{. }}\dfrac{1}{{a + \left( {n + 1} \right)d}} \\
{\text{c}}{\text{. }}\dfrac{1}{{a + \left( {n - 1} \right)d}} \\
{\text{d}}{\text{. }}\dfrac{1}{{a - \left( {n + 1} \right)d}} \\
$
Last updated date: 28th Mar 2023
•
Total views: 312k
•
Views today: 6.88k
Answer
312k+ views
Hint: - Harmonic Progression is the reciprocal of the Arithmetic Progression.
As we know that the${n^{th}}$term of an A.P is${t_n} = a + \left( {n - 1} \right)d$
So, we know that Harmonic Progression$\left( {H.P} \right)$ is the reciprocal of $\left( {A.P} \right)$
Therefore ${n^{th}}$of H.P is$ = \dfrac{1}{{{t^n}}}$
$ \Rightarrow {H_n} = \dfrac{1}{{a + \left( {n - 1} \right)d}}$
So, this is the required answer which is option c.
Note: - In such types of questions the key concept we have to remember is that${n^{th}}$term of harmonic progression is the reciprocal of arithmetic progression so, if we remember the formula of${n^{th}}$term of $\left( {A.P} \right)$ then we easily calculate the ${n^{th}}$term of$\left( {H.P} \right)$.
As we know that the${n^{th}}$term of an A.P is${t_n} = a + \left( {n - 1} \right)d$
So, we know that Harmonic Progression$\left( {H.P} \right)$ is the reciprocal of $\left( {A.P} \right)$
Therefore ${n^{th}}$of H.P is$ = \dfrac{1}{{{t^n}}}$
$ \Rightarrow {H_n} = \dfrac{1}{{a + \left( {n - 1} \right)d}}$
So, this is the required answer which is option c.
Note: - In such types of questions the key concept we have to remember is that${n^{th}}$term of harmonic progression is the reciprocal of arithmetic progression so, if we remember the formula of${n^{th}}$term of $\left( {A.P} \right)$ then we easily calculate the ${n^{th}}$term of$\left( {H.P} \right)$.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
