# en/n3EtyIaFgp0N.xml.gz
# za/n3EtyIaFgp0N.xml.gz
# en/wmlTEXvi9lgU.xml.gz
# za/wmlTEXvi9lgU.xml.gz
(src)="1"> Welcome to the presentation on finding sums of integers .
(src)="2"> You 're probably wondering why are we doing this within the context of averages .
(src)="3"> Well , if you think about it , all an average is is you take a sum of a bunch of numbers and then you divide by the number of numbers you have .
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(src)="8"> -- what is the smallest of the five integers ?
(src)="9"> Well there 's a couple of ways to do this , but I guess the most straightforward way is just to do it algebraically ,
(src)="10"> I would say .
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(src)="15"> Consecutive just means that they follow each other ,
(src)="16"> like 5 , 6 , 7 , 8 , 9 , 10 .
(src)="17"> All of those are consecutive integers , right ?
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(src)="32"> And then that 's plus 1 plus 2 is 3 , 3 plus 3 is 6 , 6 plus 4 is 10 .
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(src)="33"> So the sum of these five integers is going to be 5x plus 10 , and all I did is add up the x 's and added up the constants .
(src)="34"> And we know that that is going to equal 200 .
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(src)="35"> Now this is just a level two linear equation .
(src)="36"> We can just solve for x .
(src)="37"> So we get 5x is equal to 190 -- I just subtracted 10 from both sides , right ?
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(src)="39"> 5 goes into 19 three times , 3 times 5 is 15 .
(src)="40"> 9 minus 5 is 4 , bring down the 0 .
(src)="41"> 5 goes into 40 , eight times .
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(src)="55"> If we had a number that was much smaller than 40 or something , you couldn 't just necessarily pick the middle number .
(src)="56"> But in this case these are consecutive and makes sense .
(src)="57"> Another way we could have done this problem , if you were , say , taking the SAT and they were to ask you the sum of five numbers is 200 , what 's the average of the numbers ?
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(src)="70"> So let 's do this problem .
(src)="71"> Let 's say that x is the largest .
(src)="72"> Then what would the number right below x be ?
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(src)="74"> Well , if x is an odd number , x minus 1 would be an even number .
(src)="75"> So in order to get the number right below it , we have to do x minus 2 to get another odd number .
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(src)="76"> My apologies -- it should say the sum of seven consecutive odd .
(src)="77"> I don 't know if you assumed that .
(src)="78"> I 'm trying my best today to confuse you .
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(src)="83"> So that 's why you 're going up or down by two , depending how you view it .
(src)="84"> So the next one down would be x minus 2 , then we 'll have x minus 4 , x minus 6 , x minus 8 , x minus 10 , x minus 12 .
(src)="85"> I think that 's it .
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