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Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P?
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Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P?
Given:
Fourth term = 3/5
Eighth term = 1/3
To find the first three terms of the harmonic progression (H.P.), we need to understand the concept of a harmonic progression and use the given information to calculate the common difference between the terms.
Harmonic Progression (H.P.):
In mathematics, a harmonic progression is a sequence of numbers in which the reciprocal of each term is in arithmetic progression. In other words, the reciprocals of the terms form an arithmetic progression.
The general form of a harmonic progression is: 1/a, 1/(a+d), 1/(a+2d), ...
Where 'a' is the first term and 'd' is the common difference between the terms.
Finding the Common Difference:
To find the common difference in this problem, we can use the given information.
We are given that the fourth term of the H.P. is 3/5, which means the reciprocal of the fourth term is 5/3. Thus, the fourth term can be written as 1/(5/3) = 3/5.
Similarly, the eighth term of the H.P. is 1/3, which means the reciprocal of the eighth term is 3. Thus, the eighth term can be written as 1/3 = 1/(1/3) = 3.
From this, we can see that the common difference between the terms is 3 - 3/5 = 12/5.
Calculating the First Three Terms:
Now that we have the common difference, we can calculate the first three terms of the H.P.
The first term, 'a', can be found by subtracting '2d' from the fourth term:
a = (3/5) - 2(12/5) = (3/5) - (24/5) = -21/5.
The second term can be found by adding 'd' to the first term:
a + d = (-21/5) + (12/5) = -9/5.
The third term can be found by adding 'd' to the second term:
a + 2d = (-21/5) + 2(12/5) = (-21/5) + (24/5) = 3/5.
Final Answer:
Therefore, the first three terms of the harmonic progression are:
1st term = -21/5
2nd term = -9/5
3rd term = 3/5.
In summary:
1. The harmonic progression is a sequence of numbers where the reciprocal of each term is in arithmetic progression.
2. To find the common difference, we use the given information about specific terms of the H.P.
3. Using the common difference, we can calculate the first three terms of the H.P.
Fourth term = 3/5
Eighth term = 1/3
To find the first three terms of the harmonic progression (H.P.), we need to understand the concept of a harmonic progression and use the given information to calculate the common difference between the terms.
Harmonic Progression (H.P.):
In mathematics, a harmonic progression is a sequence of numbers in which the reciprocal of each term is in arithmetic progression. In other words, the reciprocals of the terms form an arithmetic progression.
The general form of a harmonic progression is: 1/a, 1/(a+d), 1/(a+2d), ...
Where 'a' is the first term and 'd' is the common difference between the terms.
Finding the Common Difference:
To find the common difference in this problem, we can use the given information.
We are given that the fourth term of the H.P. is 3/5, which means the reciprocal of the fourth term is 5/3. Thus, the fourth term can be written as 1/(5/3) = 3/5.
Similarly, the eighth term of the H.P. is 1/3, which means the reciprocal of the eighth term is 3. Thus, the eighth term can be written as 1/3 = 1/(1/3) = 3.
From this, we can see that the common difference between the terms is 3 - 3/5 = 12/5.
Calculating the First Three Terms:
Now that we have the common difference, we can calculate the first three terms of the H.P.
The first term, 'a', can be found by subtracting '2d' from the fourth term:
a = (3/5) - 2(12/5) = (3/5) - (24/5) = -21/5.
The second term can be found by adding 'd' to the first term:
a + d = (-21/5) + (12/5) = -9/5.
The third term can be found by adding 'd' to the second term:
a + 2d = (-21/5) + 2(12/5) = (-21/5) + (24/5) = 3/5.
Final Answer:
Therefore, the first three terms of the harmonic progression are:
1st term = -21/5
2nd term = -9/5
3rd term = 3/5.
In summary:
1. The harmonic progression is a sequence of numbers where the reciprocal of each term is in arithmetic progression.
2. To find the common difference, we use the given information about specific terms of the H.P.
3. Using the common difference, we can calculate the first three terms of the H.P.
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Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P?
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Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P? for B Com 2025 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P? covers all topics & solutions for B Com 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P?.
Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P? for B Com 2025 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P? covers all topics & solutions for B Com 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fourth term=3/5 Eighth term=1/3 Then find first three term of H.P?.
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