1. The problem states that the terms of the sequence are given by the formula $s_n = 4n + 7$ for $n = 0,1,2,3,\ldots$. 2. We need to determine whether the sequence is arithmetic or geometric and identify the initial value and common difference or ratio. 3. Recall the definitions: - An arithmetic sequence has the form $s_n = s_0 + nd$, where $d$ is the common difference. - A geometric sequence has the form $s_n = s_0 \times r^n$, where $r$ is the common ratio. 4. Given $s_n = 4n + 7$, when $n=0$, $s_0 = 4(0) + 7 = 7$. 5. To check if the sequence is arithmetic, calculate the difference between consecutive terms: $$s_1 - s_0 = (4(1) + 7) - 7 = 11 - 7 = 4$$ $$s_2 - s_1 = (4(2) + 7) - 11 = 15 - 11 = 4$$ The difference is constant at 4, so the sequence is arithmetic with common difference 4. 6. To check if the sequence is geometric, calculate the ratio between consecutive terms: $$\frac{s_1}{s_0} = \frac{11}{7} \neq 4$$ $$\frac{s_2}{s_1} = \frac{15}{11} \neq 4$$ The ratio is not constant, so the sequence is not geometric. 7. Therefore, the sequence is arithmetic with initial value 7 and common difference 4. **Final answer:** Option C.