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how many terms of the AP:9,17,25,... must be taken to give a sum of 636
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how many terms of the AP:9,17,25,... must be taken to give a sum of 63...
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how many terms of the AP:9,17,25,... must be taken to give a sum of 63...
Introduction:
To find the number of terms of an arithmetic progression (AP) that must be taken to give a sum of 636, we need to understand the concept of the sum of an AP and solve the problem using the appropriate formula.
Sum of an Arithmetic Progression:
The sum of an arithmetic progression is given by the formula:
S = (n/2)(2a + (n-1)d)
where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference.
Given Information:
First term (a) = 9
Common difference (d) = 17 - 9 = 8
Sum of the terms (S) = 636
Using the Sum of AP Formula:
We can rearrange the sum formula to solve for the number of terms (n):
S = (n/2)(2a + (n-1)d)
636 = (n/2)(2(9) + (n-1)(8))
Simplifying the equation:
636 = (n/2)(18 + 8n - 8)
636 = (n/2)(8n + 10)
Dividing both sides by 2:
318 = n(8n + 10)
318 = 8n^2 + 10n
Rearranging the equation to form a quadratic equation:
8n^2 + 10n - 318 = 0
Solving the Quadratic Equation:
To find the number of terms (n), we need to solve the quadratic equation. We can use the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 8, b = 10, and c = -318.
Using the quadratic formula, we can calculate the values of n.
To find the number of terms of an arithmetic progression (AP) that must be taken to give a sum of 636, we need to understand the concept of the sum of an AP and solve the problem using the appropriate formula.
Sum of an Arithmetic Progression:
The sum of an arithmetic progression is given by the formula:
S = (n/2)(2a + (n-1)d)
where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference.
Given Information:
First term (a) = 9
Common difference (d) = 17 - 9 = 8
Sum of the terms (S) = 636
Using the Sum of AP Formula:
We can rearrange the sum formula to solve for the number of terms (n):
S = (n/2)(2a + (n-1)d)
636 = (n/2)(2(9) + (n-1)(8))
Simplifying the equation:
636 = (n/2)(18 + 8n - 8)
636 = (n/2)(8n + 10)
Dividing both sides by 2:
318 = n(8n + 10)
318 = 8n^2 + 10n
Rearranging the equation to form a quadratic equation:
8n^2 + 10n - 318 = 0
Solving the Quadratic Equation:
To find the number of terms (n), we need to solve the quadratic equation. We can use the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 8, b = 10, and c = -318.
Using the quadratic formula, we can calculate the values of n.
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how many terms of the AP:9,17,25,... must be taken to give a sum of 636 Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics?
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how many terms of the AP:9,17,25,... must be taken to give a sum of 636 Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? 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 how many terms of the AP:9,17,25,... must be taken to give a sum of 636 Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for how many terms of the AP:9,17,25,... must be taken to give a sum of 636 Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics?.
how many terms of the AP:9,17,25,... must be taken to give a sum of 636 Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? 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 how many terms of the AP:9,17,25,... must be taken to give a sum of 636 Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for how many terms of the AP:9,17,25,... must be taken to give a sum of 636 Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics?.
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