Find the value of 1-2-3+2-3-4+...+ upto 100 terms.

-694

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-626

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-624

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-549

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Solution

The correct option is B
-626

The first 100 terms of this series can be viewed as: (1 -2 -3) + (2 - 3 - 4)+.... +(33 - 34 - 35) + 34
The first 33 terms of the above series (indicated inside the brackets) will give an A.P: -4, -5, -6 ... -36
Sum of this A.P. = $33 \times - 20 = - 660$
Answer = - 660 + 34 = - 626

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