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# Ways to find the sum of consecutive odd/even numbers

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Ways to find the sum of consecutive odd/even numbers [#permalink]  03 Nov 2005, 22:05
Hi Can anyone please give me a clarification on how to find the sum of consecutive odd/even numbers?

http://www.gmatclub.com/phpbb/viewtopic ... g+integers
ian7777 wrote:
The last thing to note is that if you have consecutive even numbers, or consecutive odds, after you subtract, you have to divide by 2, and then add one. There are 7 even integers from 22-34, because 34-12=12/2=6+1=7.

However, if I apply the same concept to find the sum of even integers from 5 to 9, inclusive, it doesn't seem to work. I was only able to find the sum of odd integers using that formula.

Are there any variations?
Thanks.
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Well the generic way to sum a set of consecutive numbers is to follow our friend Gauss approach:

Avg of First and last term * number of items in the set

for example:
1 + 2 + 3 +.. + 100

(100 + 1) / 2 * 100

2 + 4 + 6 + ...+ 200 =
(200 + 2)/2 * 100

the quoted section in your post talks about finding "number of items in the set".

for eample, in the above sequence of even numbers, there are 100 items. How do you find it? The generic way is :
(last element - first element/interval) + 1

so, for even number series like above, the number of items in the series is:
(200 - 2 / 2) + 1 = 100

The think to remember is that you should apply this when first and last element is in the set.

for example, if you are to find sum of even numbers from 1 to 99, first find first even number and last even number:
first element: 2
last element: 98

now apply above technique
Intern
Joined: 25 Jul 2005
Posts: 48
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duttsit wrote:
for example, if you are to find sum of even numbers from 1 to 99, first find first even number and last even number:
first element: 2
last element: 98

now apply above technique

Thanks I understood now.
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