In a harmonic progression, if the first term is 4 and the second term is 2, what is the common difference of the corresponding arithmetic progression?
Practice Questions
1 question
Q1
In a harmonic progression, if the first term is 4 and the second term is 2, what is the common difference of the corresponding arithmetic progression?
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The reciprocals of the terms are 1/4 and 1/2. The common difference is 1/2 - 1/4 = 1/4.
Questions & Step-by-step Solutions
1 item
Q
Q: In a harmonic progression, if the first term is 4 and the second term is 2, what is the common difference of the corresponding arithmetic progression?
Solution: The reciprocals of the terms are 1/4 and 1/2. The common difference is 1/2 - 1/4 = 1/4.
Steps: 6
Step 1: Identify the first term of the harmonic progression, which is given as 4.
Step 2: Identify the second term of the harmonic progression, which is given as 2.
Step 3: Find the reciprocals of the terms. The reciprocal of 4 is 1/4 and the reciprocal of 2 is 1/2.
Step 4: Calculate the common difference of the corresponding arithmetic progression by subtracting the first reciprocal from the second reciprocal: 1/2 - 1/4.
Step 5: Simplify the subtraction: 1/2 is equivalent to 2/4, so 2/4 - 1/4 = 1/4.
Step 6: Conclude that the common difference of the corresponding arithmetic progression is 1/4.
