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Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.
It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by ‘x* and y , then the product of the nth terms of the two progressions is:
It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by ‘x* and y , then the product of the nth terms of the two progressions is:
- a)nxy
- b)3xy x (2n - 0.5)2
- c)xy
- d)xy x [0.25 + (3/? - 1.2)2]
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two series of numbers are formed such that the first series is an arit...
Let the common difference of the AP be denoted as ‘d'.
d = y - x
The nth term of the AP = x + [(n - 1) x (y - x)] ... (i)
The first 2 terms of the HP are ‘y' and ‘x'
Hence the 1st and 2nd terms of the arithmetic progression corresponding to the HP are
From (i) and (ii) we get the product of the nth terms of the two progressions as follows:
= xy
Hence, option 3.
d = y - x
The nth term of the AP = x + [(n - 1) x (y - x)] ... (i)
The first 2 terms of the HP are ‘y' and ‘x'
Hence the 1st and 2nd terms of the arithmetic progression corresponding to the HP are
From (i) and (ii) we get the product of the nth terms of the two progressions as follows:
= xy
Hence, option 3.
Most Upvoted Answer
Two series of numbers are formed such that the first series is an arit...
To solve this problem, let's break it down step by step:
Given information:
- The first series is an arithmetic progression (AP).
- The second series is a harmonic progression (HP).
- The first term of the AP is equal to the second term of the HP.
- The first term of the HP is equal to the second term of the AP.
Step 1: Understanding Arithmetic Progression (AP)
An arithmetic progression is a series of numbers in which the difference between consecutive terms is constant. It can be represented as:
a, a + d, a + 2d, a + 3d, ...
Here, 'a' is the first term and 'd' is the common difference.
Step 2: Understanding Harmonic Progression (HP)
A harmonic progression is a series of numbers in which the reciprocals of the terms are in arithmetic progression. It can be represented as:
1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d), ...
Here, 'a' is the first term and 'd' is the common difference.
Step 3: Equating the First Terms of AP and HP
According to the given information, the first term of the AP is equal to the second term of the HP, and vice versa. Let's represent these terms as 'x*' and 'y', respectively.
a (AP) = x*
1/a (HP) = y
Step 4: Expressing the nth terms of AP and HP
The nth term of an AP can be expressed as:
a + (n - 1)d
The nth term of an HP can be expressed as:
1/(a + (n - 1)d)
Step 5: Finding the Product of nth Terms
To find the product of the nth terms of the AP and HP, we need to multiply the expressions obtained in Step 4.
Product = (a + (n - 1)d) * (1/(a + (n - 1)d))
Step 6: Substituting the Values
Now, let's substitute the values of 'a' and 'd' from Step 3 into the product expression.
Product = (x* + (n - 1)d) * (1/(x* + (n - 1)d))
Step 7: Simplifying the Product Expression
Since (x* + (n - 1)d) is common in the numerator and denominator, we can cancel it out.
Product = 1
Step 8: Final Answer
The product of the nth terms of the AP and HP is 1, which can be represented as xy.
Therefore, the correct answer is option 'C': xy.
Given information:
- The first series is an arithmetic progression (AP).
- The second series is a harmonic progression (HP).
- The first term of the AP is equal to the second term of the HP.
- The first term of the HP is equal to the second term of the AP.
Step 1: Understanding Arithmetic Progression (AP)
An arithmetic progression is a series of numbers in which the difference between consecutive terms is constant. It can be represented as:
a, a + d, a + 2d, a + 3d, ...
Here, 'a' is the first term and 'd' is the common difference.
Step 2: Understanding Harmonic Progression (HP)
A harmonic progression is a series of numbers in which the reciprocals of the terms are in arithmetic progression. It can be represented as:
1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d), ...
Here, 'a' is the first term and 'd' is the common difference.
Step 3: Equating the First Terms of AP and HP
According to the given information, the first term of the AP is equal to the second term of the HP, and vice versa. Let's represent these terms as 'x*' and 'y', respectively.
a (AP) = x*
1/a (HP) = y
Step 4: Expressing the nth terms of AP and HP
The nth term of an AP can be expressed as:
a + (n - 1)d
The nth term of an HP can be expressed as:
1/(a + (n - 1)d)
Step 5: Finding the Product of nth Terms
To find the product of the nth terms of the AP and HP, we need to multiply the expressions obtained in Step 4.
Product = (a + (n - 1)d) * (1/(a + (n - 1)d))
Step 6: Substituting the Values
Now, let's substitute the values of 'a' and 'd' from Step 3 into the product expression.
Product = (x* + (n - 1)d) * (1/(x* + (n - 1)d))
Step 7: Simplifying the Product Expression
Since (x* + (n - 1)d) is common in the numerator and denominator, we can cancel it out.
Product = 1
Step 8: Final Answer
The product of the nth terms of the AP and HP is 1, which can be represented as xy.
Therefore, the correct answer is option 'C': xy.
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Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer?
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Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer?.
Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer?.
Solutions for Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Two series of numbers are formed such that the first series is an arithmetic progression while the second is a harmonic progression.It is further known that the 1st term of the AP is equal to the 2nd term of the HP and the 1st term of the HP is equal to the 2nd term of the AP. If the first 2 terms of the AP are denoted by x* and y , then the product of the nth terms of the two progressions is:a)nxyb)3xy x (2n- 0.5)2c)xyd)xy x [0.25 + (3/? - 1.2)2]Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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