SOLUTION: All the page numbers of a book are added beginning at page one. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice? D

Algebra ->  Sequences-and-series -> SOLUTION: All the page numbers of a book are added beginning at page one. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice? D      Log On


   



Question 889429: All the page numbers of a book are added beginning at page one. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice? Do it in details.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
s = ½(2a + (n-1)d)n
a=1
d=1
1000> 1/2*(2 + (n-1))*n
highest n=44
s = ½(2 + (43))44
s = 45*22
s=990
1000-990=10
10 was repeated twice