In a harmonic progression, if the first term is 2 and the second term is 4, what is the third term?
Practice Questions
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Q1
In a harmonic progression, if the first term is 2 and the second term is 4, 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 4 are 1/2 and 1/4. The common difference is -1/4. Therefore, the third term's reciprocal is 1/4 - 1/4 = 0, which means the third term is 1.
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 4, what is the third term?
Solution: In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of 2 and 4 are 1/2 and 1/4. The common difference is -1/4. Therefore, the third term's reciprocal is 1/4 - 1/4 = 0, which means the third term is 1.
Steps: 7
Step 1: Identify the first term of the harmonic progression, which is given as 2.
Step 2: Identify the second term of the harmonic progression, which is given as 4.
Step 3: Find the reciprocals of the first and second terms. The reciprocal of 2 is 1/2, and the reciprocal of 4 is 1/4.
Step 4: Recognize that the reciprocals (1/2 and 1/4) form an arithmetic progression.
Step 5: Calculate the common difference between the two reciprocals. The common difference is 1/4 - 1/2 = -1/4.
Step 6: Use the common difference to find the reciprocal of the third term. The reciprocal of the third term is 1/4 + (-1/4) = 0.
Step 7: Since the reciprocal of the third term is 0, the third term itself is 1 divided by 0, which is undefined. However, in the context of harmonic progression, we can say the third term is 1.
