what is the sum of the numbers form -100 to 98

Question

Hello I need help with a contest question that I am not very sure about thanks.

What is the sum of the numbers from negative one hundred and ninety eight?

Answer 1

So you have the following sequence $-100, -99,-98,\ldots, 0,1,2,\ldots, 98.$

Your last term say $a_n=98$ which is equal to $$a_n=a+(n-1)d$$

$$98=-100+(n-1)\times 1$$ $$198=n-1$$ $$n=199$$

Now you have $a=-100, n=199, d=1$, use the formula you have mentioned in the comments.

Answer 2

A different approach not involving any formulas

you want to sum $$-100,-99,-98,\cdots-2,-1,0,1,2,\cdots,97,98$$

As you can see $98$ cancels out with $-98$ similarly $97$ cancels out with $-97$ and similarly, everything cancels out till 0

In the end, you are left with -100,-99,0

Thus required sum is $$-100-99=-199$$