Exercise 22 Page 318

Let's make a table that shows the length of the deer antler over time.

From the table we see that there is a common difference of

2,

so it is an arithmetic sequence. Since

d = 2,

we can write the recursive equation for the length of the deer antler.

a_{n} = a_{n - 1} + d \Rightarrow a_{n} = a_{n - 1} + \frac{1}{4}

The recursive rule is the recursive equation together with the first term.

Recursive Rule : a_{1} = 4 \frac{1}{2}, a_{n} = a_{n - 1} + \frac{1}{4}