Let's make a table that shows the lengths of the bones.
From the table, we see that the sequence does not have a common difference nor a common ratio, so it is neitherarithmetic nor geometric. However, we can write a recursive rule for it. Let's look for a pattern in the difference of consecutive terms.
a_1-a_2& = 9.5-6 = 3.5
a_2-a_3& = 6-3.5 = 2.5
We see that beginning with the third term each term is the difference of two previous terms. Hence, a recursive equation for the sequence is a_n=a_(n-2)-a_(n-1).
The first two terms and the recursive equation give us the recursive rule.
Recursive Rule:
a_1=9.5, a_2=6, a_n=a_(n-2)-a_(n-1)
b
When we measure the lengths of the different sections of our hands, we will see that there is no discernible pattern. This means that we cannot use a recursive rule to describe the lengths.
