1. **Problem statement:** We have three sequences and three expressions. We need to associate each sequence with its correct general term (term of order $n$). 2. **Sequences given:** - Sequence A: $5, 7, 9, 11, \ldots$ - Sequence B: $2, \frac{3}{4}, \frac{4}{9}, \frac{5}{16}, \ldots$ - Sequence C: $\frac{4}{3}, \frac{6}{5}, \frac{8}{7}, \frac{10}{9}, \ldots$ 3. **Expressions given:** - Expression 1: $\frac{n+1}{n^2}$ - Expression 2: $\frac{2n+2}{2n+1}$ - Expression 3: $2n + 3$ 4. **Step-by-step association:** **Sequence A:** $5, 7, 9, 11, \ldots$ - Check if it fits $2n + 3$: - For $n=1$, $2(1)+3=5$ (matches first term) - For $n=2$, $2(2)+3=7$ (matches second term) - So, Sequence A matches Expression 3: $2n + 3$ **Sequence B:** $2, \frac{3}{4}, \frac{4}{9}, \frac{5}{16}, \ldots$ - Check if it fits $\frac{n+1}{n^2}$: - For $n=1$, $\frac{1+1}{1^2} = \frac{2}{1} = 2$ (matches first term) - For $n=2$, $\frac{2+1}{2^2} = \frac{3}{4}$ (matches second term) - So, Sequence B matches Expression 1: $\frac{n+1}{n^2}$ **Sequence C:** $\frac{4}{3}, \frac{6}{5}, \frac{8}{7}, \frac{10}{9}, \ldots$ - Check if it fits $\frac{2n+2}{2n+1}$: - For $n=1$, $\frac{2(1)+2}{2(1)+1} = \frac{4}{3}$ (matches first term) - For $n=2$, $\frac{2(2)+2}{2(2)+1} = \frac{6}{5}$ (matches second term) - So, Sequence C matches Expression 2: $\frac{2n+2}{2n+1}$ 5. **Final associations:** - $5, 7, 9, 11, \ldots \rightarrow 2n + 3$ - $2, \frac{3}{4}, \frac{4}{9}, \frac{5}{16}, \ldots \rightarrow \frac{n+1}{n^2}$ - $\frac{4}{3}, \frac{6}{5}, \frac{8}{7}, \frac{10}{9}, \ldots \rightarrow \frac{2n+2}{2n+1}$