1. **Problem Statement:** Determine if the sequences generated by the given $n^{th}$ term rules are increasing, decreasing, or neither. 2. **Sequence a:** $a_n = \frac{12 - 3n}{3}$ Simplify the expression: $$a_n = \frac{12}{3} - \frac{3n}{3} = 4 - n$$ Since $a_n = 4 - n$, as $n$ increases by 1, $a_n$ decreases by 1. Therefore, sequence a is **decreasing**. 3. **Sequence b:** $b_n = \frac{n + 3}{2n + 6}$ Factor denominator: $$b_n = \frac{n + 3}{2(n + 3)}$$ Cancel common factor $n + 3$ (assuming $n \neq -3$): $$b_n = \frac{\cancel{n + 3}}{2\cancel{(n + 3)}} = \frac{1}{2}$$ Sequence b is constant at $\frac{1}{2}$, so it is **neither increasing nor decreasing**. 4. **Sequence c:** $c_n = 4n - 7$ As $n$ increases by 1, $c_n$ increases by 4. Therefore, sequence c is **increasing**. **Final answers:** - a) Decreasing - b) Neither - c) Increasing