If the nth term of a harmonic progression is given by 1/n, what is the first ter

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Question: If the nth term of a harmonic progression is given by 1/n, what is the first term?

Options:

Correct Answer: 1

Solution:

The first term corresponds to n=1, which gives 1/1 = 1.

If the nth term of a harmonic progression is given by 1/n, what is the first term?

If the nth term of a harmonic progression is given by 1/n, what is the first term?

Step 1: Understand what a harmonic progression is. It is a sequence of numbers where the reciprocals of the terms form an arithmetic progression.
Step 2: Identify the formula for the nth term of the harmonic progression given in the question, which is 1/n.
Step 3: To find the first term, set n = 1 in the formula.
Step 4: Calculate the first term by substituting n = 1 into the formula: 1/1.
Step 5: Simplify the calculation: 1/1 equals 1.
Step 6: Conclude that the first term of the harmonic progression is 1.

Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Nth Term Calculation – Understanding how to find the nth term of a sequence and applying it to find specific terms.