SOLUTION: The sum of the first n counting/natural numbers is 23005. How many numbers were added (i.e. find n)?

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Question 1059569: The sum of the first n counting/natural numbers is 23005. How many numbers were added (i.e. find n)?
Answer by ikleyn(52787) About Me  (Show Source):
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The sum of the first n counting/natural numbers is 23005. How many numbers were added (i.e. find n)?
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The sum of the first n counting/natural numbers is S%5Bn%5D = %28n%2A%28n%2B1%29%29%2F2.


See the lessons 

    - Arithmetic progressions

    - The proofs of the formulas for arithmetic progressions 

    - Problems on arithmetic progressions,  

in this site.


Therefore, to answer the question, you need to solve this equation


%28n%2A%28n%2B1%29%29%2F2 = 23005,   or


n*(n+1) = 46010.


Apply any method you know to get the answer n = 214.


(Also notice that sqrt%2846010%29 = 214.499. . . .
 It is how I got the answer).