Dholakshara is an educational system in which realm?
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Least value of n = 12
Step-by-step explanation:
As per the question
The given series
2 + 5 + 8 + 11 + .....
As we can see that the common difference is same and equals to 3.
5 - 2 = 3 = 8 - 5
Therefore,
The given series is in A.P
The sum of n terms of A.P is given by
Sum = \frac{n}{2}[2a+(n-1)d]
Where,
a = first term = 2
d = common difference = 3
Therefore,
Sum = \frac{n}{2}[2(2)+(n-1)(3)]
Sum = \frac{n}{2}[4+3n-3]
Sum = \frac{n}{2}[3n+1]
n(3n+1) ≥ 400
3n² + n - 400 ≥ 0
On solving this, we get
n ≥ 11.381
Hence, the sum for greater than 200, the least value of n = 12
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