Arithmetic Sequence Calculator Geometric Sequence Calculator Harmonic Sequence Calculator Fibonacci Sequence Calculator Number Sequence Calculator Sequence Formula Calculator Sum of Linear Number Sequence Calculator Find the sequence and next term Recursive Sequence Calculator First Five Terms of a Sequence Bound Sequence calculator Missing Terms in Arthimetic Sequence calculator Limit of Sequence Calculator Sum of Sequence Calculator Arithemetic Sequence common difference calculator Geometric Sequence Ratio Calculator Arithmetic Sequence Equation Calculator Geometric Sequence Equation Calculator Monotonic Sequence Calculator Partial Sum Arithmetic Sequence Infinite Series Calculator

Find the Sum of n terms of Harmonic Sequence a = 5, n=10, 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=10, a=5, and d = 5 easily and quickly. So that you will get the result of 1/275.0.

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

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

Sum of first 10 terms of Harmonic Sequence of a = 5, n=10, and d=5 is 0.6089

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 = 5

Put values into formula

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

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

S10 = 0.6089

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=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 = 10/2[2*5 + (10 − 1) × 5].
  • Simplify the equation, i.e., Sn = 10/2[2*5 + (10-1) × 5] = 275.0
  • At last , the sum of n terms of Arithmetic progression is 275.0.
  • Finally, the result of sum of n terms of Harmonic sequence is 1/275.0

Example for Finding Sum of n terms of Harmonic Sequence

Sum of n terms of HP when a = 5, d = 5 and n = 9
Sum of n terms of HP when a = 4, d = 2 and n = 10
Sum of n terms of HP when a = 2, d = 4 and n = 7
Sum of n terms of HP when a = 2, d = 4 and n = 7
Sum of n terms of HP when a = 1, d = 4 and n = 10
Sum of n terms of HP when a = 3, d = 3 and n = 7
Sum of n terms of HP when a = 1, d = 2 and n = 10
Sum of n terms of HP when a = 1, d = 5 and n = 9
Sum of n terms of HP when a = 4, d = 5 and n = 7
Sum of n terms of HP when a = 5, d = 4 and n = 11

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

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

sum of n terms of harmonic sequence for a = 5, n=10, and d=5 is 1/275.0.

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

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