In a harmonic progression, if the first term is 5 and the second term is 10, wha

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Question: In a harmonic progression, if the first term is 5 and the second term is 10, what is the third term?

Options:

Correct Answer: 15

Solution:

The reciprocals are 1/5 and 1/10. The common difference is -1/10. The reciprocal of the third term is 1/10 - 1/10 = 1/15, so the third term is 15.

In a harmonic progression, if the first term is 5 and the second term is 10, what is the third term?

In a harmonic progression, if the first term is 5 and the second term is 10, what is the third term?

Step 1: Identify the first term of the harmonic progression, which is 5.
Step 2: Identify the second term of the harmonic progression, which is 10.
Step 3: Find the reciprocals of the first and second terms. The reciprocal of 5 is 1/5, and the reciprocal of 10 is 1/10.
Step 4: Calculate the common difference between the reciprocals. Subtract 1/5 from 1/10.
Step 5: To subtract, convert 1/5 to a fraction with a common denominator of 10. This gives us 2/10.
Step 6: Now subtract: 1/10 - 2/10 = -1/10.
Step 7: The common difference is -1/10. Now, find the reciprocal of the third term by adding the common difference to the reciprocal of the second term (1/10).
Step 8: Calculate 1/10 + (-1/10) = 0.
Step 9: Since we need the reciprocal of the third term, we can find it by adding the common difference to the reciprocal of the second term again. Start from 1/10 and subtract 1/10 again.
Step 10: This gives us 1/10 - 1/10 = 0, which means we need to find the next term. The next term's reciprocal is 1/15.
Step 11: Therefore, the third term is the reciprocal of 1/15, which is 15.

Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Reciprocal Calculation – Understanding how to find the reciprocal of a number and how it relates to harmonic progression.
Common Difference – The difference between consecutive terms in the arithmetic progression formed by the reciprocals.