SOLUTION: Dada opened a book randomly and began adding every seventh page number beginning with the number on the page to which she had opened, until she added twenty-one page numbers. If t

Question 113694: Dada opened a book randomly and began adding every seventh page number beginning with the number on the page to which she had opened, until she added twenty-one page numbers. If the total she obtained was 1995, to what page did she open?
Found 2 solutions by checkley71, Adam:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
S=N/2(A+L) WHERE N=THE NUMBER OF TERMS, A=THE FIRST TERM & L=THE LAST TERM.
1995=21/2(A+A+20*7) HERE THE LAST PAGE NUMBER IS THE FIRST PAGE +20*7=140.
1995=21/2(2A+140)
1995=21A+21*70
1995=21A+1470
21A=1995-1470
21A=525
A=525/21
A=25 ANSWER FOR THE NUMBER OF THE FIRST PAGE.
Answer by Adam(64) (Show Source): You can put this solution on YOUR website!
We can rewrite her addition as sequence.
A0 = x (page where she opened the book)
An+1 = A0 + 7
the formula for summation of first n terms is defined as
we use formula for nth term , we use A0 for Ar =>
An = A0+n*d
An = x+n*7
n = 21 thus An = x+147
we substitute this into our summation formula and get

sum is the number she ended up with(1995)

that is simple linear equation which can be solved for x = 18

Adam

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