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

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?

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.