Find the Sum of n terms of Harmonic Sequence a = 4, n=9, and d=5
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=4, and d = 5 easily and quickly. So that you will get the result of 1/216.0.
Sum of first 9 terms of Harmonic Sequence of a = 4, n=9, and d=5 is 0.6868
Steps to find sum of n terms of harmonic sequence:
sum of n terms of harmonic sequence formula:-
Sn = `(1/d)*ln( (2*a+(2*n-1)*d)/(2*a-d) )`
where:
- sn is the sum of n terms
- a is first term
- n is total number of terms
- d is common difference
Input values are:-
a = 4
n = 9
d = 5
Put values into formula
S9 = `(1/d)*ln( (2*a+(2*n-1)*d)/(2*a-d) )`
S9 = `(1/5)*ln( (2*4+(2*9-1)*5)/(2*4-5) )`
S9 = 0.6868
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 = 4, n=9, and d=5.
- 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*4 + (9 − 1) × 5].
- Simplify the equation, i.e., Sn = 9/2[2*4 + (9-1) × 5] = 216.0
- At last , the sum of n terms of Arithmetic progression is 216.0.
- Finally, the result of sum of n terms of Harmonic sequence is 1/216.0
Example for Finding Sum of n terms of Harmonic Sequence
FAQs on Computing Sum of N terms for Harmonic Sequence for a = 4, n=9, and d=5
1. How to find the sum of n terms of harmonic sequence for a = 4, n=9, and d=5?
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 = 4, n=9, and d=5?
sum of n terms of harmonic sequence for a = 4, n=9, and d=5 is 1/216.0.
3. Where can I find the step by step process for sum of n terms of harmonic sequence a = 4, n=9, and d=5?
You can find the detailed steps for sum of n terms of harmonic sequence a = 4, n=9, and d=5 on our page.