Which of the following sequences cannot be a harmonic progression?
Practice Questions
Q1
Which of the following sequences cannot be a harmonic progression?
1, 1/2, 1/3
2, 4, 8
3, 1, 1/3
5, 10, 15
Questions & Step-by-Step Solutions
Which of the following sequences cannot be a harmonic progression?
Step 1: Understand what a harmonic progression (HP) is. A sequence is in HP if the reciprocals of its terms form an arithmetic progression (AP).
Step 2: Identify the given sequence: 2, 4, 8.
Step 3: Find the reciprocals of the terms in the sequence: 1/2, 1/4, 1/8.
Step 4: Check if the reciprocals form an arithmetic progression. To do this, calculate the differences between consecutive terms: (1/4 - 1/2) and (1/8 - 1/4).
Step 5: Calculate the first difference: 1/4 - 1/2 = -1/4.
Step 6: Calculate the second difference: 1/8 - 1/4 = -1/8.
Step 7: Compare the two differences. Since -1/4 is not equal to -1/8, the differences are not constant.
Step 8: Conclude that the reciprocals do not form an arithmetic progression, so the original sequence 2, 4, 8 cannot be a harmonic progression.
