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Consecutive Even Integers - Sum

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Joined: 31 Dec 1969
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Consecutive Even Integers - Sum [#permalink] New post 01 Jun 2008, 15:19
I would post the question but, it isn't reappearing in my review mode for gmatprep. But I have stumbled across this type of question and cannot seem to figure it out.

How do you find the sum of a consecutive set of even integers? MGMAT explains how to find the sum of a consecutive set of integers, but I am not sure how to go about it if it is only the even numbers or odd numbers? Also how would you alter it if they are inclusive or exclusive, let's say for the sake of this question - what is the sum of the inclusive set of even integers in the number set 101-202?

Thanks in advance!
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Re: Consecutive Even Integers - Sum [#permalink] New post 01 Jun 2008, 16:35
Basically....you want to find all the numbers in the set divisible by 2....So divide the 1st and last number of the set by 2. Then find the #s of terms in this new set....then find the average of the first and last # of the original set. Multiple that average times that # of terms in the "divided by 2" set...and you have your sum.
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Re: Consecutive Even Integers - Sum [#permalink] New post 01 Jun 2008, 16:55
jlola21 wrote:
I would post the question but, it isn't reappearing in my review mode for gmatprep. But I have stumbled across this type of question and cannot seem to figure it out.

How do you find the sum of a consecutive set of even integers? MGMAT explains how to find the sum of a consecutive set of integers, but I am not sure how to go about it if it is only the even numbers or odd numbers? Also how would you alter it if they are inclusive or exclusive, let's say for the sake of this question - what is the sum of the inclusive set of even integers in the number set 101-202?

Thanks in advance!


You would approach it just like any other consecutive integer sum problem except for one difference. You need to find two things:
1. The number of terms between the two integers in question. This is slightly different then with basic consecutive integers. You would first subtract the first term from the last, divide by 2 and then add 1--> ((last - first)/2) +1
2. The average of the terms (which is also the median in this case). This is the same as usual--> just add the first and last term together and divide by 2.

Then multiply the two answers together.

Example. What is the sum of all consecutive integers between 1 and 303? Really this is asking for the sum of all consecutive integers between 2 and 302 (since 1 and 303 are not even). So first you would find the number of even terms between 2 and 302 inclusive --> ((302 - 2)/2) + 1 =151. Then you would find the average of all the terms between 2 and 302 --> (302 + 2)/2 = 152. Then you would multiply 152 * 151 = 22,952 for the answer.

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Re: Consecutive Even Integers - Sum   [#permalink] 01 Jun 2008, 16:55
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