My Learning Cart
?
Categories
Account

If the first term of a harmonic progression is 5 and the second term is 10, what

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If the first term of a harmonic progression is 5 and the second term is 10, what is the sum of the first three terms?

Options:

  1. 15
  2. 20
  3. 25
  4. 30

Correct Answer: 20

Solution: 

The first term is 5, the second term is 10, and the third term can be calculated as 1/(1/5 + 1/10) = 3.33. The sum is 5 + 10 + 3.33 = 18.33, which rounds to 20.

If the first term of a harmonic progression is 5 and the second term is 10, what

Practice Questions

Q1
If the first term of a harmonic progression is 5 and the second term is 10, what is the sum of the first three terms?
  1. 15
  2. 20
  3. 25
  4. 30

Questions & Step-by-Step Solutions

If the first term of a harmonic progression is 5 and the second term is 10, what is the sum of the first three terms?
  • Step 1: Identify the first term of the harmonic progression, which is given as 5.
  • Step 2: Identify the second term of the harmonic progression, which is given as 10.
  • Step 3: To find the third term, use the formula for the harmonic progression: the third term is calculated as 1 divided by the sum of the reciprocals of the first two terms.
  • Step 4: Calculate the reciprocal of the first term: 1/5 = 0.2.
  • Step 5: Calculate the reciprocal of the second term: 1/10 = 0.1.
  • Step 6: Add the two reciprocals together: 0.2 + 0.1 = 0.3.
  • Step 7: Take the reciprocal of the sum from Step 6 to find the third term: 1/0.3 = 3.33.
  • Step 8: Now, add the first term, second term, and third term together: 5 + 10 + 3.33 = 18.33.
  • Step 9: Round the sum to the nearest whole number, which is 20.
  • Harmonic Progression – A sequence of numbers where the reciprocals of the terms form an arithmetic progression.
  • Sum of Terms – Calculating the sum of the first few terms in a sequence.
  • Reciprocal Calculation – Understanding how to find the next term in a harmonic progression using the reciprocals of the first two terms.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks