In a harmonic progression, if the first term is 1 and the second term is 1/2, wh

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Question: In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the sum of the first three terms?

Options:

Correct Answer: 3

Solution:

The first term is 1, the second term is 1/2, and the third term can be calculated as 1/(1 + 1/2) = 2/3. The sum is 1 + 1/2 + 2/3 = 2.

In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the sum of the first three terms?

In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the sum of the first three terms?

Step 1: Identify the first term of the harmonic progression, which is given as 1.
Step 2: Identify the second term of the harmonic progression, which is given as 1/2.
Step 3: To find the third term, use the formula for harmonic progression: the third term is 1 divided by the sum of the reciprocals of the first two terms.
Step 4: Calculate the sum of the reciprocals of the first two terms: 1 + 1/2 = 3/2.
Step 5: Now, find the third term: it is 1 divided by 3/2, which is the same as multiplying by 2/3. So, the third term is 2/3.
Step 6: Now, add the first three terms together: 1 + 1/2 + 2/3.
Step 7: To add these fractions, find a common denominator, which is 6. Convert each term: 1 = 6/6, 1/2 = 3/6, and 2/3 = 4/6.
Step 8: Now add them: 6/6 + 3/6 + 4/6 = 13/6.
Step 9: The final answer is the sum of the first three terms, which is 13/6.

Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Sum of Terms – Calculating the sum of the first few terms in a sequence.