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### Best Answer Jessee R says

Following the basics of Arithmetic progression we can use the formula of summation and apply here as in the figure

We can then solve it in 5 simple arithmetic steps

logically we can also see that (-1) will occur 50 times in the series as in

(1-2)(3-4)(5-6) and so on... so the result will be 50 multiplied by -1 hence -50

### Ben Evans says

The quick way to do it is:

Lets look at the average of consecutive odd integers which are all positive:

1+99=100/2=50 (this average works because: 1+99=100, 3+97=100, and 5+95=100......and so on These will all average to 50.

All the negative numbers are even. So the average of the even number are (-2 + -100)/2=-51

So the average times the number of numbers composing the average will give us the sum.

50(50) +50(-51) is the sum and this equals 50(50-51)= -50

### Larry Wall says

We use to call them lollipops in school back in the 50s. They were assigned in the lower grades, but we started at 100, subtract 2, then add 1, subtract 2, add 1 and so on. It would pretty much kill a recess.