+1833
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. For the price of the book at the extreme right, a customer can buy the middle book and a book adjacent to the middle one. Give an expression for the cost of the nth book in terms of n.
+128521 Let the price of the first book = P........then we have the following series:
an = P + 2(n - 1) where an is the price of the nth book
I assume that you want to know the price of the 31st book??
a31 = P + 2(31 - 1) = P + 2(30) = $ [P + 60]
The cost of the middle book - the 16th one - is given by
a16 = P + 2(16 -1) = P + 2(15) = $ [P + 30]
However........it is not possible to buy the middle book and an adjacent book for the price of the 31st book
The price of the 15th book = $ [ P + 28] and the price of the 17th book = $ [P + 32]
The cost of buying the middle book and the 15th book = $ [ 2P + 58] which may or may not be greater than the cost of the 31st book. But, the cost of buying the middle book and the 17th book = $ [2P + 62] which is definitely greater than the cost of the 31st book.
P. S.- I hope I have interpreted this correctly !!!!
