(1) The first and thirteenth terms of an arithmetic sequence are 5 and 29, respectively. What is the fiftieth term?
(2) The pages of a book are numbered through . When the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of . What was the number of the page that was added twice?
+240 (1) The first term can be labeled as x, the second x + y, third x + 2y, and so on. The 13th would be x + 12y, and the 1st would be just x.
\(x + 12y = 29 \\ x = 5 \\ 12y = 24 \\ y = 2\)
The 15th term would be x + 14y,
\(x + 14y \\ 5 + 14(2) \\ 5 + 28 = 33\)
So the 15th term would be 33.
(2) The numbers do not show, but here: https://artofproblemsolving.com/wiki/index.php/1986_AIME_Problems/Problem_6
For the 1st one I was looking for the 50th term not the 15th sorry, but thanks anyways!
(2) Sorry I don't know why the numbers did not work.
The pages of a book are numbered 1 through n. When the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of 1986. What was the number of the page that was added twice?
