Question

Fill in the blank with the recursive function. Be sure to include the starting point.

Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time.
The recursive function that gives the number of books Ashley has at any time is
=
, starting at
.

Answer 1

The recursive function that represents the number of books Ashley has at any time is

`a_n=a_(n-1)-n`

starting at

`a_1=100`

Explanation:

Ashley has 100 books that she wants to give away at the rate of n books per week.

So,

`a_1=100\\ \\a_2=100-n=a_1-n\\ \\a_3=a_2-n\\ \\...\\ \\a_n=a_(n-1)-n`

Thus, the recursive function that represents the number of books Ashley has at any time is

`a_n=a_(n-1)-n`

starting at

`a_1=100`