Question

Sum of first 'n' even numbers is n(n+1). How many even numbers from the beginning in the order makes the mean 51 ?​

Answer 1

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Answer 2

Given,

Sum of first n even numbers is n(n+1)

To find,

Number of even numbers to make the mean 51.

Solution,

Mean = ∑ sum of observations/ number of observations.

Let us suppose, $a$ even numbers give us the mean of 51.

Sum of first a even numbers ∑ $a_{i}$ = $a(a + 1)$

Total number of observations = $a$

Mean of the given data = ∑$\frac{a_{i} }{a} = \frac{a(a + 1)}{a} = a+1$

$a + 1$ is also equal to 51.

This gives us,

                   $a + 1 = 51\\a = 50$

Therefore, first 50 even numbers will give a mean of 51.