In a harmonic progression, if the first term is 3 and the second term is 6, what
Practice Questions
Q1
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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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.
