Find the Sum of n terms of Harmonic Sequence a = 5, n=10, and d=2

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=10, a=5, and d = 2 easily and quickly. So that you will get the result of 1/140.0.

First term [a]:
common difference[d]:
Total terms[n]:

Find the Sum of n terms of Harmonic Sequence a = 5, n=10, and d=2

Sum of first 10 terms of Harmonic Sequence of a = 5, n=10, and d=2 is 0.89588

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 = 5

n = 10

d = 2

Put values into formula

S10 = `(1/d)*ln( (2*a+(2*n-1)*d)/(2*a-d) )`

S10 = `(1/2)*ln( (2*5+(2*10-1)*2)/(2*5-2) )`

S10 = 0.89588

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 = 5, n=10, and d=2.
  • 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 = 10/2[2*5 + (10 − 1) × 2].
  • Simplify the equation, i.e., Sn = 10/2[2*5 + (10-1) × 2] = 140.0
  • At last , the sum of n terms of Arithmetic progression is 140.0.
  • Finally, the result of sum of n terms of Harmonic sequence is 1/140.0

Example for Finding Sum of n terms of Harmonic Sequence

Sum of n terms of HP when a = 3, d = 2 and n = 11
Sum of n terms of HP when a = 4, d = 4 and n = 6
Sum of n terms of HP when a = 3, d = 2 and n = 10
Sum of n terms of HP when a = 2, d = 4 and n = 6
Sum of n terms of HP when a = 5, d = 3 and n = 8
Sum of n terms of HP when a = 5, d = 2 and n = 10
Sum of n terms of HP when a = 4, d = 4 and n = 10
Sum of n terms of HP when a = 3, d = 3 and n = 6
Sum of n terms of HP when a = 4, d = 3 and n = 11
Sum of n terms of HP when a = 3, d = 3 and n = 8

FAQs on Computing Sum of N terms for Harmonic Sequence for a = 5, n=10, and d=2

1. How to find the sum of n terms of harmonic sequence for a = 5, n=10, and d=2?

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 = 5, n=10, and d=2?

sum of n terms of harmonic sequence for a = 5, n=10, and d=2 is 1/140.0.

3. Where can I find the step by step process for sum of n terms of harmonic sequence a = 5, n=10, and d=2?

You can find the detailed steps for sum of n terms of harmonic sequence a = 5, n=10, and d=2 on our page.