Question

the sum of n consecutive integers is 11 if the least of these integers is -10 what's the value of n

Answer 1

Answer:

You must start with -2. You have 45 numbers which is odd, so to get an even number from a sum the beginning must be even. Next 900 divided by 45 is 20. So if you have 44 complementary pairs that add to 20, and 1 number that is 20, you could get to 900. But we only have 22 so we need to be centered at 40. That is to say when you have 40 numbers left to add you should be adding 0, and you need to complement to 40. 0 inclusive you need 45 digits. That is to say that you need to sum from -n to 40+n where 40 + 2n is 44. So the only solution is to sum from -2 to 42.