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Charlize accidentally omitted two consecutive integers when adding the elements of the arithmetic sequence, $\{1, 2, 3, \ldots, n\}$. If the sum she obtained is $241$, what is the smallest possible value of $n$?

Guest Sep 28, 2017
 #1
avatar+90053 
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Note that the sum of the first 21 integers  is   21 * 22 /2  =  231...this isn't large enough

 

And the sum of the first  22 integers  =   22 * 23 / 2  =   253

 

So    253 - 241  =  12 = omitted sum.....  but  the sum of two consecutive integers must be odd

 

And......the sum of the first 23 integers is  23 * 24 / 2  = 276

 

So.......276 - 241   =  35    = omitted sum

 

So....the   consecutive integers omitted must be  17  and 18

 

So....... the smallest value of n  is   23

 

 

 

cool cool cool

CPhill  Sep 28, 2017

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