The sum of all numbers from 1 to n is n(1+n)/2, what is the

Question

The sum of all numbers from 1 to n is n(1+n)/2, what is the total of whole even numbers bigger than 99 but smaller than 301？

foraj · Answer

So the series starts from 100 and ends at 300, therefore n=101.

101(100+300)/2 = 20200.(Correction for even numbers only)

ian7777 · Answer

This is a set of consecutive numbers. Questions like to come out and give some precedent that actually makes it harder to work with. This formula is a nonstarter, because it involves only lists that go from 1 to n. Ours is a list of evens from 100-300, no relevence to the first sentence of the problem.

It's better to just know what to do with consecutives.  The sum of any consecutve list is the middle number times the number of numbers.  That needs to be clear as YOU WILL HAVE ONE QUESTION ON THE TEST ABOUT THIS.

So, how do we find those two numbers (middle and number of numbers)?

 Middle 
The middle number is always the average of the two endpoints. So starting at 100 and ending at 300, the average of those two numbers is 200. That's the middle.

 Number of Numbers 
That's just the inclusive rule you probably already know. How many even numbers are there between 100 and 300 inclusive? Three steps:

1. Subtract: 300-100=200
2. Divide by 2 (because we only want the even ones): 200/2=100
3. Add 1 (because we need to include 300, subtracting gets rid of it): 100+1=101.

 now multiply 
200x101=20,200.

This works because the middle number is the average. No matter what the question, it'll always work out.

The sum of all numbers from 1 to n is n(1+n)/2, what is the

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