Question 1154916: Simon lost his library card and has an overdue library book. When the book was 5 days late, he owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was 21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book. Suppose the total amount Simon owes when the book is n days late can be determined by an arithmetic sequence.
a↓5 ( 5 is below a) =
a↓21 ( 21 is below a )=
so …
d =
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! arithmetic sequence is An = A1 + (n-1) * d
when n = 5, A5 = A1 + (5-1) * d
when n = 21, A21 = A1 + 21-1) * d
simplify these equations to get:
A5 = A1 + 4d
A21 = A1 + 20d
since A5 = 2.25 and A21 = 6.25, you get:
2.25 = A1 + 4d
6.25 = A1 + 20d
subtract the second equation from the first to get:
4.00 = 16d
solve for d to get:
d = 4.00 / 16 = .25
when d = .25 and n = 5 and A5 = 2.25, you get:
2.25 = A1 + (5-1) * .25
simplify to get:
2.25 = A1 + 4 * .25
simplify further to get:
2.25 = A1 + 1
solve for A1 to get A1 = 1.25
when d = .25 and n = 21 and A21 = 6.25, you get:
6.25 = A1 + (21-1) * .25
simplify to get:
6.25 = A1 + 20 * .25
simplify further to get:
6.25 = A1 + 5
solve for A1 to get A1 = 1.25
d = .25 is the common difference.
both equations are true when d = .25
the general equation is An = A1 + (n-1) * d
d = .25 should be the answer to your question.
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