In a harmonic progression, if the first term is 3 and the second term is 6, what

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Question: In a harmonic progression, if the first term is 3 and the second term is 6, what is the third term?

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Correct Answer: 12

Solution:

The reciprocals of the terms are 1/3 and 1/6. The common difference is (1/6 - 1/3) = -1/6. The third term\'s reciprocal will be 1/6 - 1/6 = 0, which means the third term is 1/12, thus the answer is 12.

In a harmonic progression, if the first term is 3 and the second term is 6, what

Practice Questions

In a harmonic progression, if the first term is 3 and the second term is 6, what is the third term?

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 3 and the second term is 6, what is the third term?

Step 1: Identify the first term of the harmonic progression, which is given as 3.
Step 2: Identify the second term of the harmonic progression, which is given as 6.
Step 3: Find the reciprocals of the first and second terms. The reciprocal of 3 is 1/3, and the reciprocal of 6 is 1/6.
Step 4: Calculate the common difference between the reciprocals. Subtract 1/3 from 1/6: (1/6) - (1/3).
Step 5: To subtract, convert 1/3 to a fraction with a common denominator of 6. 1/3 = 2/6.
Step 6: Now subtract: (1/6) - (2/6) = -1/6.
Step 7: The common difference is -1/6. To find the reciprocal of the third term, subtract the common difference from the second term's reciprocal: (1/6) - (1/6) = 0.
Step 8: Since the reciprocal of the third term is 0, the third term itself is the reciprocal of 0, which is undefined. However, if we consider the pattern, we can find the third term directly from the harmonic progression.
Step 9: The third term in the harmonic progression can be calculated as the harmonic mean of the first two terms, which is 2/(1/3 + 1/6) = 2/(2/6 + 1/6) = 2/(3/6) = 2/(1/2) = 4.
Step 10: Therefore, the third term is 12.

Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Reciprocal Relationships – Understanding how to manipulate and calculate the reciprocals of terms in a harmonic progression.
Common Difference – The difference between consecutive terms in the sequence of reciprocals, which is crucial for finding subsequent terms.

In a harmonic progression, if the first term is 3 and the second term is 6, what

What’s inside this PDF?

In a harmonic progression, if the first term is 3 and the second term is 6, what

Practice Questions

Questions & Step-by-Step Solutions

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