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How many terms of an ap 45,39,33,.must be taken so thier sum is 180?
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How many terms of an ap 45,39,33,.must be taken so thier sum is 180?
Okk
a = 45
D = -6
Sn = n / 2 ( 2a + (n-1) d)
180 = n/2 ( 2*45 + (-6n +6)
360 = n ( 90 - 6n + 6)
360 = n ( 96 - 6n)
360 = 96 n - 6n^2
6n^2 - 96n + 360 = 0............1
Solve This equation U will Get Ur Answer
a = 45
D = -6
Sn = n / 2 ( 2a + (n-1) d)
180 = n/2 ( 2*45 + (-6n +6)
360 = n ( 90 - 6n + 6)
360 = n ( 96 - 6n)
360 = 96 n - 6n^2
6n^2 - 96n + 360 = 0............1
Solve This equation U will Get Ur Answer
Community Answer
How many terms of an ap 45,39,33,.must be taken so thier sum is 180?
Problem Statement
Find out how many terms of an AP 45, 39, 33, ... must be taken so that their sum is 180.
Explanation
Here, we need to find the number of terms of an AP whose sum is 180. To solve this problem, we can use the formula for the sum of n terms of an AP:
Sn = n/2 [2a + (n - 1)d]
where Sn is the sum of n terms of the AP, a is the first term, d is the common difference between the terms, and n is the number of terms.
Solution
Let's apply the formula to the given AP:
Sn = n/2 [2a + (n - 1)d]
Sn = n/2 [2(45) + (n - 1)(-6)]
Sn = n/2 [90 - 6n + 6]
Sn = n/2 [96 - 6n]
Simplifying further, we get:
Sn = 48n - 3n2
Now, we need to find out the value of n for which Sn = 180. So we can set up the equation:
48n - 3n2 = 180
3n2 - 48n + 180 = 0
Solving this quadratic equation, we get:
n = 6 or 10
So, we need to take either 6 or 10 terms of the given AP to get a sum of 180.
Conclusion
We can conclude that to get a sum of 180, we need to take either 6 or 10 terms of the given AP. This problem can be solved easily using the formula for the sum of n terms of an AP.
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How many terms of an ap 45,39,33,.must be taken so thier sum is 180?
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How many terms of an ap 45,39,33,.must be taken so thier sum is 180? for Class 10 2025 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 an ap 45,39,33,.must be taken so thier sum is 180? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many terms of an ap 45,39,33,.must be taken so thier sum is 180?.
How many terms of an ap 45,39,33,.must be taken so thier sum is 180? for Class 10 2025 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 an ap 45,39,33,.must be taken so thier sum is 180? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many terms of an ap 45,39,33,.must be taken so thier sum is 180?.
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