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The average of the squares of first ten natural numbers is-
Answer & Solution
Correct Answer:
Option
D
As we know that average of square of "n" natural number is
$$\eqalign{ & = \frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{{6n}} \cr & = \frac{{\left( {n + 1} \right)\left( {2n + 1} \right)}}{6} \cr} $$
According to the question,
Average of square of first ten natural number is
$$\eqalign{ & = \frac{{\left( {10 + 1} \right)\left( {20 + 1} \right)}}{6} \cr & = \frac{{11 \times 21}}{6} \cr & = 38.5 \cr} $$
$$\eqalign{ & = \frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{{6n}} \cr & = \frac{{\left( {n + 1} \right)\left( {2n + 1} \right)}}{6} \cr} $$
According to the question,
Average of square of first ten natural number is
$$\eqalign{ & = \frac{{\left( {10 + 1} \right)\left( {20 + 1} \right)}}{6} \cr & = \frac{{11 \times 21}}{6} \cr & = 38.5 \cr} $$
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