If the first term of a harmonic progression is 1 and the common difference of th

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?

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?

Step 1: Understand that a harmonic progression (HP) is formed by taking the reciprocals of the terms of an arithmetic progression (AP).
Step 2: The first term of the HP is given as 1. This means the first term of the corresponding AP is 1 (since 1 is the reciprocal of 1).
Step 3: The common difference of the AP is given as 1. This means each term in the AP increases by 1 from the previous term.
Step 4: Calculate the second term of the AP. Since the first term is 1 and the common difference is 1, the second term of the AP is 1 + 1 = 2.
Step 5: The second term of the HP is the reciprocal of the second term of the AP. Therefore, the second term of the HP is 1 / 2.
Step 6: Conclude that the second term of the harmonic progression is 1/2.

Harmonic Progression (HP) – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Arithmetic Progression (AP) – A sequence of numbers is in arithmetic progression if the difference between consecutive terms is constant.
Reciprocal Relationship – In a harmonic progression, the terms are related to the arithmetic progression through their reciprocals.