In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
Practice Questions
1 question
Q1
In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
1/2
1/4
1/6
1/8
The reciprocals are 1 and 2, which are in arithmetic progression with a common difference of 1/2.
Questions & Step-by-step Solutions
1 item
Q
Q: In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
Solution: The reciprocals are 1 and 2, which are in arithmetic progression with a common difference of 1/2.
Steps: 7
Step 1: Understand that a harmonic progression (HP) is a sequence of numbers whose reciprocals form an arithmetic progression (AP).
Step 2: Identify the first term of the HP, which is given as 1.
Step 3: Identify the second term of the HP, which is given as 1/2.
Step 4: Find the reciprocals of the HP terms: the reciprocal of 1 is 1, and the reciprocal of 1/2 is 2.
Step 5: Now we have the first two terms of the corresponding AP: 1 and 2.
Step 6: Calculate the common difference of the AP by subtracting the first term from the second term: 2 - 1 = 1.
Step 7: Therefore, the common difference of the corresponding arithmetic progression is 1.
