If the first term of a harmonic progression is 1 and the second term is 1/2, wha
Practice Questions
Q1
If the first term of a harmonic progression is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
1/2
1/4
1/3
1
Questions & Step-by-Step Solutions
If the first term of a harmonic progression is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
Step 1: Understand that a harmonic progression (HP) is a sequence of numbers whose reciprocals form an arithmetic progression (AP).
Step 2: Identify the first term of the HP, which is given as 1. The reciprocal of 1 is 1.
Step 3: Identify the second term of the HP, which is given as 1/2. The reciprocal of 1/2 is 2.
Step 4: Now we have the first two terms of the corresponding AP: 1 and 2.
Step 5: To find the common difference of the AP, subtract the first term from the second term: 2 - 1 = 1.
Step 6: Therefore, the common difference of the corresponding arithmetic progression is 1.
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.
Common Difference – The constant difference between consecutive terms in an arithmetic progression.
