# How do you find the sum of all numbers from 1 to 100 by using patterns and combinations & shorter easier way?

It's for my son's hw this is what the page states

"The objective of this activity is to find the sum of all the counting numbers from 1 to 100. You could certainly add 1 + 2 + 3 continuing to 100 to find the sum. However, this is too much work for this problem. If you can look for patterns and combinations, you can find a much shorter and easier way to solve this problem. Try to work smarter, not longer.

Answer 1 plus all the numbers up to 100 __________

now sum 1 to 200 as well

Answer 2 plus all the numbers up to 200 __________

Thanks for your help

### 4 Answers

- Merisa.Lv 410 years agoFavorite Answer
Hey!

To find the sum of consecutive integers, you must first find the middle number. To do this, you add the first and last number, and divide by two.

1 + 100 / 2 = 55.5

Next, you must find the number of numbers (last number - first number + 1), which is 100 in this case.

And finally, you simply multiply the two numbers together.

55.5*100 = 5550

Therefore the sum of all the numbers is 5550!

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- Anonymous10 years ago
This is the formula:

(1 + n)*(n/2)

n = The number of numbers

So:

Up to 100: (1+100)* (100/2) = 101*50 = 5,050

Up to 200: (1+200)*(200/2) = 201*100 = 20,100

Source(s): A* Maths iGCSE- Login to reply the answers

- grippoLv 43 years ago
arithmetic series formula (including numbers): a(n) = a1 + d(n - a million) a(n) = a million + a million(n - a million) a(n) = n Sum of an arithmetic series: S(n) = n/2 * (a1 + an) S(one hundred) = 50 * (a million + one hundred) S(one hundred) = 5,050 S(2 hundred) = one hundred * (a million + 2 hundred) S(2 hundred) = 20,one hundred

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- AlyssaLv 410 years ago
This should help: http://mathforum.org/library/drmath/view/57919.htm...

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