In a harmonic progression, if the first term is 2 and the second term is 3, what is the third term?
Practice Questions
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In a harmonic progression, if the first term is 2 and the second term is 3, what is the third term?
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In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of 2 and 3 are 1/2 and 1/3. The common difference is 1/3 - 1/2 = -1/6. The third term's reciprocal will be 1/3 - 1/6 = 1/6, so the third term is 6.
Questions & Step-by-step Solutions
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Q
Q: In a harmonic progression, if the first term is 2 and the second term is 3, what is the third term?
Solution: In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of 2 and 3 are 1/2 and 1/3. The common difference is 1/3 - 1/2 = -1/6. The third term's reciprocal will be 1/3 - 1/6 = 1/6, so the third term is 6.
Steps: 6
Step 1: Identify the first term of the harmonic progression, which is 2.
Step 2: Identify the second term of the harmonic progression, which is 3.
Step 3: Find the reciprocals of the first and second terms. The reciprocal of 2 is 1/2, and the reciprocal of 3 is 1/3.
Step 4: Calculate the common difference between the reciprocals. Subtract 1/2 from 1/3: 1/3 - 1/2 = -1/6.
Step 5: To find the reciprocal of the third term, add the common difference (-1/6) to the reciprocal of the second term (1/3): 1/3 - 1/6 = 1/6.
Step 6: The reciprocal of the third term is 1/6, so the third term itself is the reciprocal of 1/6, which is 6.
