If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?
Practice Questions
1 question
Q1
If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?
1/6
1/3
1/2
1
The reciprocals are 1, 2, and 3. The common difference is 2 - 1 = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?
Solution: The reciprocals are 1, 2, and 3. The common difference is 2 - 1 = 1.
Steps: 5
Step 1: Identify the first three terms of the harmonic progression, which are 1, 1/2, and 1/3.
Step 2: Find the reciprocals of these terms. The reciprocal of 1 is 1, the reciprocal of 1/2 is 2, and the reciprocal of 1/3 is 3.
Step 3: Write down the new sequence formed by the reciprocals: 1, 2, and 3.
Step 4: Determine the common difference in this new sequence. The common difference is found by subtracting the first term from the second term: 2 - 1 = 1.
Step 5: Conclude that the common difference of the corresponding arithmetic progression is 1.
