## Thinking Mathematically (6th Edition)

(i) The sequence is arithmetic. (ii) The next two terms are: $2$ and $\frac{7}{3}$.
A sequence is: (a) arithmetic if there is a common difference among the terms. (b) geometric if there is a common ratio among the terms. Notice that the given sequence has terms that increase by $\frac{1}{3}$. This means that the sequence has a common difference of $\frac{1}{3}$. Thus, the sequence is $\underline{\text{arithmetic}}$. The next two terms can be found by adding $\frac{1}{3}$ to the previous term. Therefore, the next two terms are: $\frac{5}{3} + \frac{1}{3} =\frac{6}{3}=2 \\2 + \frac{1}{3} = \frac{7}{3}$