A  leaf  is  torn  from  a  paperback  novel. The  sum  of  the  numbers  on  the  remaining  pages  is 15000.  What are the page numbers on the torn leaf ?

2 years ago

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Answers : (1)

                                        Hello student,
Please find the answer to your question below
The sum of the numbers form an arithmetic progression.
So, assuming the number of pages is n, the first is number 1. And number missing are p and p+1 (a leaf is torn so two page numbers missing).
Then Sum of all pages= n/2 (2+n-1) {using the formula of sum of AP with a=1}
The Sum of remaining pages =15000=n/2(2+n-1)-p-(p+1);
=> 15000= n+n^2/2-n/2-2p-1
=> 15000=n^2/2+n/2-2p-1
=>14999*2=n^2+n-4p
=>4p=n^2+n-14999*2
=>p=(n^2+n-14999*2)*0.25
=>p=(n(n+1)-14999*2)*0.25
Thus knowing the total number of pages you can determine p and p+1 numerically.
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