What is the relationship between the terms of a harmonic progression and their r
Practice Questions
Q1
What is the relationship between the terms of a harmonic progression and their reciprocals?
They are in geometric progression.
They are in arithmetic progression.
They are in quadratic progression.
They are in exponential progression.
Questions & Step-by-Step Solutions
What is the relationship between the terms of a harmonic progression and their reciprocals?
Step 1: Understand what a harmonic progression (HP) is. It is a sequence of numbers where the reciprocals of the terms form an arithmetic progression (AP).
Step 2: Know what an arithmetic progression (AP) is. It is a sequence of numbers where the difference between consecutive terms is constant.
Step 3: If you have a harmonic progression, for example, the terms are a1, a2, a3,..., then their reciprocals are 1/a1, 1/a2, 1/a3,...
Step 4: Recognize that if 1/a1, 1/a2, 1/a3,... form an arithmetic progression, it means that the original terms a1, a2, a3,... form a harmonic progression.
Step 5: Conclude that the relationship is that the terms of a harmonic progression are the reciprocals of the terms of an arithmetic progression.
