SOLUTION: If the ages of the students in Class XI are inA.P. with common differnce three months and the age of the youngest student is 16 years . Find the number of students in class XI , if

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Question 725194: If the ages of the students in Class XI are inA.P. with common differnce three months and the age of the youngest student is 16 years . Find the number of students in class XI , if the sum of ages of students in 861 .
Answer by stanbon(75887) About Me  (Show Source):
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If the ages of the students in Class XI are inA.P. with common differnce three months and the age of the youngest student is 16 years . Find the number of students in class XI , if the sum of ages of students in 861 .
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a(1) = 16 years
d = 3/12 = 1/4
Sum = 861 years
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a(n) = a(1) + (n-1)d
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S(n) = (n/2)(a(1) + a(n)
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861 = (n/2)(16 + 16+(n-1)(1/4))
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861 = (n/2)(32 + (n-1)(1/4)
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861 = 16n + (n^2-n)(1/8)
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6888 = 128n + n^2-n
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n^2 + 127n - 6888 = 0
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n = 41
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cheers,
Stan H.
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