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Three numbers 5, p and 10 are in Harmonic progression if p = ?
- a)10/3
- b)20/3
- c)3/10
- d)3/20
Correct answer is option 'B'. Can you explain this answer?
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Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)...
Concept:
Three numbers x, y, and z are in H.P if and only if y 
Calculation:
Calculation:
Given: Three numbers 5, p and 10 are in Harmonic progression
Now, According to the concept used
Now, According to the concept used
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Community Answer
Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)...
Harmonic Progression:
Harmonic progression is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression. In simpler terms, if three numbers a, b, and c are in harmonic progression, then 1/a, 1/b, and 1/c are in arithmetic progression.
Given:
- Three numbers 5, p, and 10 are in harmonic progression.
Calculating the Harmonic Mean (H):
- The Harmonic Mean (H) of three numbers a, b, and c is given by:
H = 3/(1/a + 1/b + 1/c)
Substitute the given numbers:
- Given a = 5, b = p, and c = 10, we can substitute these values into the formula:
H = 3/(1/5 + 1/p + 1/10)
Calculate the Harmonic Mean:
- Simplifying the expression, we get:
H = 3/((10 + 10p + 5)/(10p))
H = 3*(10p)/(15 + 10p)
Given that the numbers are in harmonic progression:
- Since the numbers 5, p, and 10 are in harmonic progression, the Harmonic Mean (H) must be equal to p:
p = 3*(10p)/(15 + 10p)
Solve for p:
- Cross-multiply to solve for p:
p(15 + 10p) = 3*(10p)
15p + 10p^2 = 30p
10p^2 - 15p + 30p = 0
10p^2 + 15p = 0
p(10p + 15) = 0
p = 0 or p = -15/10
Answer:
Therefore, the value of p that satisfies the condition is p = 20/3.
Harmonic progression is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression. In simpler terms, if three numbers a, b, and c are in harmonic progression, then 1/a, 1/b, and 1/c are in arithmetic progression.
Given:
- Three numbers 5, p, and 10 are in harmonic progression.
Calculating the Harmonic Mean (H):
- The Harmonic Mean (H) of three numbers a, b, and c is given by:
H = 3/(1/a + 1/b + 1/c)
Substitute the given numbers:
- Given a = 5, b = p, and c = 10, we can substitute these values into the formula:
H = 3/(1/5 + 1/p + 1/10)
Calculate the Harmonic Mean:
- Simplifying the expression, we get:
H = 3/((10 + 10p + 5)/(10p))
H = 3*(10p)/(15 + 10p)
Given that the numbers are in harmonic progression:
- Since the numbers 5, p, and 10 are in harmonic progression, the Harmonic Mean (H) must be equal to p:
p = 3*(10p)/(15 + 10p)
Solve for p:
- Cross-multiply to solve for p:
p(15 + 10p) = 3*(10p)
15p + 10p^2 = 30p
10p^2 - 15p + 30p = 0
10p^2 + 15p = 0
p(10p + 15) = 0
p = 0 or p = -15/10
Answer:
Therefore, the value of p that satisfies the condition is p = 20/3.
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Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)20/3c)3/10d)3/20Correct answer is option 'B'. Can you explain this answer?
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