Exercise 2 Page 318

We are given the rules shown below and we are asked to find the one that is different. Recall that a rule can be explicit when it gives the $n\text{th}$ term, $a_n,$ as a function of the term's position number $n.$ Or, it is recursive if it gives the first term or terms, and a recursive equation that tells how $a_n$ is related to the preceding terms. Let's take a second look at the rules given and identify which of them are recursive rules. As we can see, all the rules are recursive since they give a first term and a recursive equation, except for $a_n=6n-2.$ This rule is explicit, as it just gives an equation for $a_n$ in terms of the term's position. Therefore, this is the different one.