Thirty-one books are arranged from left to right in order of increasing prices. The price of each book differs by $2 from that of each adjacent book. The price of the book at the extreme right is equal to the price of the middle book plus a book adjacent to the middle one. Give an expression for the cost of the $n$th book in terms of $n$.
Let the middle book cost x dollars. The book to the left costs x-2 and the one to the right costs x+2. The last book, 15 to right of the middle, costs x + 30 dollars. Let's consider two cases: Case 1: The last book costs the same as the middle book and one to its right. Then x + (x+2) = x + 30 x = 28
However, this means the leftmost book costs x-30 = -2 dollars, which is unlikely. Case 2: The last book costs the same as the middle book and one to its left. Then x + (x-2) = x + 30 x = 32
In this case, the costs of the books are $2, $4, $62. The nth book costs 2n dollars.
