What will be the sum of $1 - 2 + 3 - 4 + 5 - 6 . . . . .$ when last integer is $21 ?$

$31$

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$11$

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$- 10$

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$- 31$

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Solution

The correct option is B
$11$

the sum of $1 - 2 + 3 - 4 + 5 - 6 . . . . .$ when last integer is $21$ $\begin{array}{rcl} = & 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 + 17 - 18 + 19 - 20 + 21 \\ = & (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21) - 2 - 4 - 6 - 8 - 10 - 12 - 14 - 16 - 18 - 20 \\ = & 121 - (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) \\ = & 121 - 110 \\ = & 11 \end{array}$
Hence, the correct option is (b) $11$ .

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