If the first term of a harmonic progression is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
Practice Questions
1 question
Q1
If the first term of a harmonic progression is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
1/2
1/4
1/3
1
The reciprocals are 1 and 2, which have a common difference of 1.
Questions & Step-by-step Solutions
1 item
Q
Q: If the first term of a harmonic progression 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 have a common difference of 1.
Steps: 6
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. The reciprocal of 1 is 1.
Step 3: Identify the second term of the HP, which is given as 1/2. The reciprocal of 1/2 is 2.
Step 4: Now we have the first two terms of the corresponding AP: 1 and 2.
Step 5: To find the common difference of the AP, subtract the first term from the second term: 2 - 1 = 1.
Step 6: Therefore, the common difference of the corresponding arithmetic progression is 1.
