A picnic group for Shimla consists of students whose ages are in A.P., the common difference being 3 months. If the youngest student Neerajis just 12 years old and the sum of ages of all students is 375 years. Findthe number of students in the group
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In this A.P ;
a = 12 years = 12×12 = 144 months
d = 3 months
Sn = 375 years = 375×12 = 4500 months
n = ?
Sn = n/2(2a+(n-1)d
4500 = n/2 (2×144 + (n-1)3)
9000 = n (288 + 3n -3)
9000 = 3n^2 + 285n
n^2 + 95n - 3000 = 0
n^2 -25n +120n -3000 = 0
n(n-25) +120(n-25) = 0
(n+120) (n-25) = 0
n = -120 & 25
as number is students can never be negative,
So number of students in the group will be 25.
hope this helped you .......................!
a = 12 years = 12×12 = 144 months
d = 3 months
Sn = 375 years = 375×12 = 4500 months
n = ?
Sn = n/2(2a+(n-1)d
4500 = n/2 (2×144 + (n-1)3)
9000 = n (288 + 3n -3)
9000 = 3n^2 + 285n
n^2 + 95n - 3000 = 0
n^2 -25n +120n -3000 = 0
n(n-25) +120(n-25) = 0
(n+120) (n-25) = 0
n = -120 & 25
as number is students can never be negative,
So number of students in the group will be 25.
hope this helped you .......................!
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