If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is

If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?

If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?

Step 1: Identify the first three terms of the harmonic progression, which are 1, 1/2, and 1/3.
Step 2: Find the reciprocals of these terms. The reciprocal of 1 is 1, the reciprocal of 1/2 is 2, and the reciprocal of 1/3 is 3.
Step 3: Write down the new sequence formed by the reciprocals: 1, 2, and 3.
Step 4: Determine the common difference in this new sequence. The common difference is found by subtracting the first term from the second term: 2 - 1 = 1.
Step 5: Conclude that 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 numbers 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 harmonic and arithmetic progressions through their reciprocals.