If the first term of a harmonic progression is 4 and the common difference of th

If the first term of a harmonic progression is 4 and the common difference of the corresponding arithmetic progression is 2, what is the second term?

If the first term of a harmonic progression is 4 and the common difference of the corresponding arithmetic progression is 2, what is the second term?

Step 1: Identify the first term of the harmonic progression, which is given as 4.
Step 2: Find the reciprocal of the first term. The reciprocal of 4 is 1/4.
Step 3: Identify the common difference of the corresponding arithmetic progression, which is given as 2.
Step 4: Add the common difference (2) to the reciprocal of the first term (1/4). This gives us: 1/4 + 2.
Step 5: Convert 2 into a fraction with a denominator of 4. So, 2 = 8/4.
Step 6: Now add the two fractions: 1/4 + 8/4 = 9/4.
Step 7: The second term of the harmonic progression is the reciprocal of 9/4. The reciprocal is 4/9.

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 manipulate and calculate the reciprocals of terms in harmonic and arithmetic progressions.