Question

A collection of books is set up into 34 rows. The first row has 96 books, and each row after that one

has 2 less books than the preceding row. (a) How many total books are there in the structure and (b)
how many books are in the 17th row?

Answer 1

a(17) = 64

Explanation:

you can create an arithmetic sequence formula as follows:

a(n) = a(1) + d(n-1) where a(1) is the first value and d is the common difference

a(17) = 96 -2(17-1)

a(17) = 96 - 32

a(17) = 64

Answer 2

Part A: 3197

Part B: 62

Explanation:

Part A: To make this easier just multiply 96 books by 34 rows which is 3264 books, but then since you are taking away 2 books for every row, multiply 2 by the 34 rows which is 68 but since the first row starts at 96 we will take away 1 row from the 68 which is 67. Then subtract 67 from the 3264 books and get 3197 books.

Part B: To make this easier just multiply 17 by 2 since we know for every row, 2 books are taken away and that equals 34 so subtract 34 from 96 and get 62.