# Find the Sum of n terms of Harmonic Sequence a = 3, n=9, and d=3

**Created By :** Abhinandan Kumar

**Reviewed By :** Phani Ponnapalli

**Last Updated :** Mar 23, 2023

Utilize our **Harmonic sequence calculator** tool for finding the sum of n terms of harmonic sequence when n=9, a=3, and d = 3 easily and quickly. So that you will get the result of 1/135.0.

## Sum of first 9 terms of Harmonic Sequence of a = 3, n=9, and d=3 is 0.98148

Steps to find sum of n terms of harmonic sequence:

**sum of n terms of harmonic sequence formula:-**

S_{n} = `(1/d)*ln( (2*a+(2*n-1)*d)/(2*a-d) )`

**where:**

- s
_{n}is the sum of n terms - a is first term
- n is total number of terms
- d is common difference

**Input values are:-**

a = 3

n = 9

d = 3

**Put values into formula**

S_{9} = `(1/d)*ln( (2*a+(2*n-1)*d)/(2*a-d) )`

S_{9} = `(1/3)*ln( (2*3+(2*9-1)*3)/(2*3-3) )`

**S _{9} = 0.98148**

Following are the step by step process to find the sum of N terms in a harmonic sequence easily by hand.

- Firstly, Write down the values that were given in the problem, such as a = 3, n=9, and d=3.
- As we know that arithmetic progression is the reciprocal of harmonic progression.
- Apply the formula of sum of n term of Arithmetic Progression, i.e., Sn = n/2[2a + (n − 1) × d]
- Substitute the values in the formula, i.e., Sn = 9/2[2*3 + (9 − 1) × 3].
- Simplify the equation, i.e., Sn = 9/2[2*3 + (9-1) × 3] = 135.0
- At last , the sum of n terms of Arithmetic progression is 135.0.
- Finally, the result of sum of n terms of Harmonic sequence is 1/135.0

### Example for Finding Sum of n terms of Harmonic Sequence

### FAQs on Computing Sum of N terms for Harmonic Sequence for a = 3, n=9, and d=3

**1. How to find the sum of n terms of harmonic sequence for a = 3, n=9, and d=3?**

As we know that the reciprocal of arithmetic progression is the harmonic sequence, find the sum of n terms of arithmetic progression and then make a reciprocal. So that you will get the sum of n terms of harmonic sequence.

**2. What is the sum of n terms of harmonic sequence for a = 3, n=9, and d=3?**

sum of n terms of harmonic sequence for a = 3, n=9, and d=3 is 1/135.0.

**3. Where can I find the step by step process for sum of n terms of harmonic sequence a = 3, n=9, and d=3?**

You can find the detailed steps for sum of n terms of harmonic sequence a = 3, n=9, and d=3 on our page.