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Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number?
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Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P wit...
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Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1.
(a) Find the value of x:
- In a geometric progression (G.P), the common ratio r is given by the formula: r = (second term) / (first term).
- Therefore, in this case, the common ratio r = 9 / (7-2x).
- Also, the third term in the G.P is given by the formula: (first term) * r^2 = (5x+17).
- Substituting the values, we get: (7-2x) * (9 / (7-2x))^2 = 5x+17.
- Simplifying the equation gives us a quadratic equation in terms of x, which can be solved to find the value of x.
(b) Find the smaller number:
- Let the two positive numbers be 3x and 4x (since they are in the ratio 3:4).
- According to the given condition, 3*(3x) + 2*(4x) = 68.
- Solving this equation gives us the value of x.
- Once x is found, the smaller number can be calculated by substituting the value of x back into 3x.
Thus, by following these steps, we can find the value of x and the smaller number as required in the given problem.
Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1.
(a) Find the value of x:
- In a geometric progression (G.P), the common ratio r is given by the formula: r = (second term) / (first term).
- Therefore, in this case, the common ratio r = 9 / (7-2x).
- Also, the third term in the G.P is given by the formula: (first term) * r^2 = (5x+17).
- Substituting the values, we get: (7-2x) * (9 / (7-2x))^2 = 5x+17.
- Simplifying the equation gives us a quadratic equation in terms of x, which can be solved to find the value of x.
(b) Find the smaller number:
- Let the two positive numbers be 3x and 4x (since they are in the ratio 3:4).
- According to the given condition, 3*(3x) + 2*(4x) = 68.
- Solving this equation gives us the value of x.
- Once x is found, the smaller number can be calculated by substituting the value of x back into 3x.
Thus, by following these steps, we can find the value of x and the smaller number as required in the given problem.
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Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number?
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Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number?.
Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that (7-2x), 9, (5x+17) are three consecutive terms of a G.P with ratio r>1, (a)find the value of x (b) two positive numbers are in ratio 3:4, fine the sum of the thrice the first number and twice the second number is 68. find the smaller number?.
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