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The mean of the first ten even natural number is-
Answer & Solution
Correct Answer:
Option
C
Required mean
$$\eqalign{ & = \left( {\frac{{2 + 4 + 6 + ..... + 20}}{{10}}} \right) \cr & = \frac{{2\left( {1 + 2 + ..... + 10} \right)}}{{10}} \cr} $$
$$ = \left( {\frac{1}{5} \times \frac{{10 \times 11}}{2}} \right)$$ $$\left[ {\because 1 + 2 + 3 + ... + n = \frac{{n\left( {n + 1} \right)}}{2}} \right]$$
$$ = 11$$
$$\eqalign{ & = \left( {\frac{{2 + 4 + 6 + ..... + 20}}{{10}}} \right) \cr & = \frac{{2\left( {1 + 2 + ..... + 10} \right)}}{{10}} \cr} $$
$$ = \left( {\frac{1}{5} \times \frac{{10 \times 11}}{2}} \right)$$ $$\left[ {\because 1 + 2 + 3 + ... + n = \frac{{n\left( {n + 1} \right)}}{2}} \right]$$
$$ = 11$$
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