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Ways to find the sum of consecutive odd/even numbers

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Intern
Joined: 25 Jul 2005
Posts: 48
Ways to find the sum of consecutive odd/even numbers  [#permalink]

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03 Nov 2005, 23:05
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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Director
Joined: 21 Aug 2005
Posts: 741

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03 Nov 2005, 23:14
VP
Joined: 22 Aug 2005
Posts: 1045
Location: CA

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03 Nov 2005, 23:18
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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03 Nov 2005, 23:33
1
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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This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Joined: 09 Sep 2013
Posts: 11005
Re: Ways to find the sum of consecutive odd/even numbers  [#permalink]

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29 Aug 2018, 04:24
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Re: Ways to find the sum of consecutive odd/even numbers   [#permalink] 29 Aug 2018, 04:24
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