If the mean of nobsenrations12 ,22,32………n2 is 46n11, then n is equal to

A
11
B
12
C
23
D
22

Solution:

According to the given condition,

$\begin{array}{l} \frac{1^{2} + 2^{2} + 3^{2} + \dots + n^{2}}{n} = \frac{46 n}{11} \\ \Rightarrow \frac{n (n + 1) (2 n + 1)}{6 n} = \frac{46 n}{11} \\ \Rightarrow 11 (2 n^{2} + 3 n + 1) = 276 n \\ \Rightarrow 22 n^{2} - 243 n + 11 = 0 \\ \Rightarrow (n - 11) (22 n - 1) = 0 \\ \Rightarrow n = 11 \end{array}$

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