If the first term of a harmonic progression is 1 and the common difference of th
Practice Questions
Q1
If the first term of a harmonic progression is 1 and the common difference of the corresponding arithmetic progression is 2, what is the second term of the harmonic progression?
1/2
1/3
1/4
1/5
Questions & Step-by-Step Solutions
If the first term of a harmonic progression is 1 and the common difference of the corresponding arithmetic progression is 2, what is the second term of the harmonic progression?
Step 1: Understand that a harmonic progression (HP) is related to an arithmetic progression (AP). The terms of an HP are the reciprocals of the terms of an AP.
Step 2: Identify the first term of the HP, which is given as 1.
Step 3: Since the first term of the HP is 1, the first term of the corresponding AP is the reciprocal of 1, which is also 1.
Step 4: The common difference of the AP is given as 2. This means to find the second term of the AP, we add the common difference to the first term: 1 + 2 = 3.
Step 5: The second term of the HP is the reciprocal of the second term of the AP. Since the second term of the AP is 3, the second term of the HP is 1/3.
Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Arithmetic Progression – A sequence of numbers is in arithmetic progression if the difference between consecutive terms is constant.
Reciprocal Relationship – The terms of a harmonic progression are the reciprocals of the terms of the corresponding arithmetic progression.
