In a harmonic progression, if the first term is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
Practice Questions
1 question
Q1
In a harmonic progression, if the first term is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
2.5
3.33
4
6
The first term is 5, and the second term in the harmonic progression corresponds to the reciprocal of the second term in the arithmetic progression, which is 5 + 2 = 7. Thus, the second term is 1/7.
Questions & Step-by-step Solutions
1 item
Q
Q: In a harmonic progression, if the first term is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
Solution: The first term is 5, and the second term in the harmonic progression corresponds to the reciprocal of the second term in the arithmetic progression, which is 5 + 2 = 7. Thus, the second term is 1/7.
Steps: 8
Step 1: Identify the first term of the harmonic progression, which is given as 5.
Step 2: Understand that the harmonic progression is related to an arithmetic progression (AP).
Step 3: The first term of the corresponding arithmetic progression (AP) is also 5.
Step 4: The common difference of the AP is given as 2.
Step 5: Calculate the second term of the AP by adding the common difference to the first term: 5 + 2 = 7.
Step 6: The second term of the harmonic progression corresponds to the reciprocal of the second term of the AP.
Step 7: Calculate the reciprocal of 7: 1/7.
Step 8: Conclude that the second term of the harmonic progression is 1/7.
