Verified Answer :
1 book is 17.55
2 books is 16.70
3 books is 15.85
4 books is 15
5 books is 4.15
6 books is 4.30
7 books is (3.55)
The cost for each book will be \(\boxed{\$ 12.45}\) if the person buy 7 books.
Further explanation:
The arithmetic sequence can be expressed as follows,
\({a_1}, {a_2}, {a_3}\)......
Here,\(a{\text{ or }}{a_1}\) represents the first term, \({a_2}\) represents the second term, and so on.
The common difference “d” can be obtained as follows,
\(\boxed{d = {a_2} - {a_1}}\)
The nth term can be obtained as follows,
\(\boxed{{a_n} = a + \left( {n - 1} \right)d}\)
Explanation:
The cost of a book is \(\$ 17.55.\)
The cost of a book is \(\$ 16.70\) if the person buys 2 books.
The cost of a book is \(\$ 15.85\) if the person buys 3 books.
The cost of a book is \(\$ 15.00\) if the person buys 4 books.
The sequence is \(\$ 17.55, \$ 16.70, \$ 15.85, \$ 15.00.\)
The first term is \(\$ 17.55,\) the second term is \(\$ 16.70.\)
The common difference “d” can be obtained as follows,
\(\begin{aligned}d&={a_2} - {a_1}\\&=16.70 - 17.55\\&=- 0.85\\\end{aligned}\)
The cost for each book if the person buys 7 books can be obtained as follows,
\(\begin{aligned}{a_6}&= 17.55 + \left( {7 - 1} \right)\left( { - 0.85} \right)\\&= 17.55 + 6\left({ - 0.85} \right)\\&= 17.55 - 5.1\\&=\$12.45\\\end{aligned}\)
The cost for each book will be \(\boxed{\$ 12.45}\) if the person buy 7 books.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Arithmetic Sequence
Keywords: Store, books, price, $17.55, 2 books, 3 books each cost $16.40, pattern continues, cost, 7 books.