If the first term of a harmonic progression is 3 and the second term is 6, what

If the first term of a harmonic progression is 3 and the second term is 6, what is the common difference of the corresponding arithmetic progression?

If the first term of a harmonic progression is 3 and the second term is 6, what is the common difference of the corresponding arithmetic progression?

Step 1: Identify the first term of the harmonic progression (HP), which is given as 3.
Step 2: Identify the second term of the harmonic progression (HP), which is given as 6.
Step 3: Find the reciprocals of the first and second terms. The reciprocal of 3 is 1/3, and the reciprocal of 6 is 1/6.
Step 4: Calculate the common difference of the corresponding arithmetic progression (AP) by subtracting the first reciprocal from the second reciprocal: 1/6 - 1/3.
Step 5: To perform the subtraction, convert 1/3 to a fraction with a common denominator of 6. This gives us 1/3 = 2/6.
Step 6: Now subtract: 1/6 - 2/6 = -1/6.
Step 7: The common difference of the arithmetic progression is -1/6.

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 Relationships – Understanding how to convert between harmonic and arithmetic progressions using reciprocals.