Which of the following sequences is a harmonic progression?
Practice Questions
Q1
Which of the following sequences is a harmonic progression?
1, 2, 3
1, 1/2, 1/3
2, 4, 6
3, 6, 9
Questions & Step-by-Step Solutions
Which of the following sequences is a harmonic progression?
Step 1: Understand what a harmonic progression is. A harmonic progression is a sequence of numbers where the reciprocals of the numbers form an arithmetic progression.
Step 2: Identify the sequence given in the question. In this case, the sequence is 1, 1/2, 1/3.
Step 3: Find the reciprocals of the numbers in the sequence. The reciprocals of 1, 1/2, and 1/3 are 1, 2, and 3 respectively.
Step 4: Check if the reciprocals form an arithmetic progression. An arithmetic progression is a sequence where the difference between consecutive terms is constant. Here, the difference between 2 and 1 is 1, and the difference between 3 and 2 is also 1.
Step 5: Since the differences are constant, the reciprocals 1, 2, 3 are in arithmetic progression.
Step 6: Conclude that since the reciprocals are in arithmetic progression, the original sequence 1, 1/2, 1/3 is a harmonic progression.
