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If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers?
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If sum of four consecutive numbers in an AP is 32 the ratio of the pro...
Here mine ans is..2,6,10..and 14..as told by manoj u will get a=8..an a.c..to further condition..you will get d=2..
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If sum of four consecutive numbers in an AP is 32 the ratio of the pro...
Explanation:
Given:
Sum of four consecutive numbers in an AP is 32.
The ratio of the product of the first and the last term to the product of two middle terms is 7:15.
Let's assume the four consecutive numbers in the AP are:
a, a + d, a + 2d, a + 3d
Sum of the four consecutive numbers:
a + (a + d) + (a + 2d) + (a + 3d) = 32
4a + 6d = 32
2a + 3d = 16
Product of the first and the last term:
a * (a + 3d)
Product of the two middle terms:
(a + d) * (a + 2d)
Ratio of the products:
(a * (a + 3d)) / ((a + d) * (a + 2d)) = 7 / 15
(a^2 + 3ad) / (a^2 + 3ad + 2d^2) = 7 / 15
15a^2 + 45ad = 7a^2 + 21ad + 14d^2
8a^2 + 24ad - 14d^2 = 0
2a^2 + 6ad - 3d^2 = 0
Solving the equations:
2a^2 + 6ad - 3d^2 = 0
a(2a + 3d) - d(2a + 3d) = 0
(a - d)(2a + 3d) = 0
a = d or a = -1.5d
Since the numbers are positive, a = d
Substitute back into 2a + 3d = 16
2d + 3d = 16
5d = 16
d = 3.2
Therefore, the four consecutive numbers are:
a = 3.2, a + d = 6.4, a + 2d = 9.6, a + 3d = 12.8
Given:
Sum of four consecutive numbers in an AP is 32.
The ratio of the product of the first and the last term to the product of two middle terms is 7:15.
Let's assume the four consecutive numbers in the AP are:
a, a + d, a + 2d, a + 3d
Sum of the four consecutive numbers:
a + (a + d) + (a + 2d) + (a + 3d) = 32
4a + 6d = 32
2a + 3d = 16
Product of the first and the last term:
a * (a + 3d)
Product of the two middle terms:
(a + d) * (a + 2d)
Ratio of the products:
(a * (a + 3d)) / ((a + d) * (a + 2d)) = 7 / 15
(a^2 + 3ad) / (a^2 + 3ad + 2d^2) = 7 / 15
15a^2 + 45ad = 7a^2 + 21ad + 14d^2
8a^2 + 24ad - 14d^2 = 0
2a^2 + 6ad - 3d^2 = 0
Solving the equations:
2a^2 + 6ad - 3d^2 = 0
a(2a + 3d) - d(2a + 3d) = 0
(a - d)(2a + 3d) = 0
a = d or a = -1.5d
Since the numbers are positive, a = d
Substitute back into 2a + 3d = 16
2d + 3d = 16
5d = 16
d = 3.2
Therefore, the four consecutive numbers are:
a = 3.2, a + d = 6.4, a + 2d = 9.6, a + 3d = 12.8
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If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers?
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If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers?.
If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of four consecutive numbers in an AP is 32 the ratio of the product of the first and the last term to the product of two middle terms is 7:15.Find the numbers?.
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