In a harmonic progression, if the first term is 4 and the second term is 8, what is the common difference of the corresponding arithmetic progression?
Practice Questions
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Q1
In a harmonic progression, if the first term is 4 and the second term is 8, what is the common difference of the corresponding arithmetic progression?
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The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8, which means the common difference of the corresponding arithmetic progression is 1/8.
Questions & Step-by-step Solutions
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Q
Q: In a harmonic progression, if the first term is 4 and the second term is 8, what is the common difference of the corresponding arithmetic progression?
Solution: The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8, which means the common difference of the corresponding arithmetic progression is 1/8.
Steps: 8
Step 1: Understand that a harmonic progression (HP) is related to an arithmetic progression (AP) through their reciprocals.
Step 2: Identify the first term of the HP, which is given as 4. The reciprocal of 4 is 1/4.
Step 3: Identify the second term of the HP, which is given as 8. The reciprocal of 8 is 1/8.
Step 4: Write down the reciprocals: the first term is 1/4 and the second term is 1/8.
Step 5: Calculate the common difference of the corresponding arithmetic progression by subtracting the first reciprocal from the second reciprocal: 1/8 - 1/4.
Step 6: To subtract, convert 1/4 to have a common denominator with 1/8. The common denominator is 8, so 1/4 becomes 2/8.
Step 7: Now perform the subtraction: 1/8 - 2/8 = -1/8.
Step 8: The common difference of the corresponding arithmetic progression is -1/8.
