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 1, 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 1, what is the second term of the harmonic progression?
Step 1: Understand that a harmonic progression (HP) is formed from the reciprocals of an arithmetic progression (AP).
Step 2: Identify the first term of the HP, which is given as 1.
Step 3: Recognize that the corresponding arithmetic progression has a common difference of 1.
Step 4: The first term of the AP is the reciprocal of the first term of the HP, which is 1. So, the first term of the AP is 1.
Step 5: Calculate the second term of the AP by adding the common difference (1) to the first term (1): 1 + 1 = 2.
Step 6: The second term of the HP is the reciprocal of the second term of the AP. So, take the reciprocal of 2: 1/2.
Step 7: Conclude that the second term of the harmonic progression is 1/2.
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 – Understanding the relationship between terms in harmonic and arithmetic progressions through their reciprocals.
