In a harmonic progression, if the first term is 5 and the second term is 10, 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 5 and the second term is 10, what is the common difference of the corresponding arithmetic progression?
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The reciprocals are 1/5 and 1/10. The common difference is 1/10 - 1/5 = -1/10, which is the difference in the arithmetic progression.
Questions & Step-by-step Solutions
1 item
Q
Q: In a harmonic progression, if the first term is 5 and the second term is 10, what is the common difference of the corresponding arithmetic progression?
Solution: The reciprocals are 1/5 and 1/10. The common difference is 1/10 - 1/5 = -1/10, which is the difference in the arithmetic progression.
Steps: 8
Step 1: Understand that a harmonic progression (HP) is related to an arithmetic progression (AP) through the reciprocals of its terms.
Step 2: Identify the first term of the HP, which is 5. The reciprocal of 5 is 1/5.
Step 3: Identify the second term of the HP, which is 10. The reciprocal of 10 is 1/10.
Step 4: Write down the reciprocals: the first term is 1/5 and the second term is 1/10.
Step 5: Calculate the common difference of the corresponding arithmetic progression (AP) by subtracting the first reciprocal from the second reciprocal: 1/10 - 1/5.
Step 6: To perform the subtraction, convert 1/5 to a fraction with a common denominator of 10: 1/5 = 2/10.
Step 7: Now subtract: 1/10 - 2/10 = -1/10.
Step 8: The result, -1/10, is the common difference of the corresponding arithmetic progression.
