Consider the sequence of numbers: \( \frac{3}{8}, \frac{3}{4}, 1 \frac{1}{8}, 1 \frac{1}{2}, 1 \frac{7}{8}, \ldots \) Which statement is a description of the sequence? The sequence is recursive, where each term is \( \frac{1}{4} \) greater than its preceding term. The sequence is recursive and can be represented by the function \( f(n+1)=f(n)+\frac{3}{8} \). The sequence is arithmetic, where each pair of terms has a constant difference of \( \frac{3}{4} \). The sequence is arithmetic and can be represented by the function \( f(n+1)=f(n)\left(\frac{3}{8}\right) \).

To analyze the sequence, first observe that: • The first term is 3/8. • The second term is 3/4, which is 3/8 + 3/8. • The third term is 1 1/8 (which is 9/8), and 9/8 – 6/8 (which is 3/4) equals 3/8. • This pattern continues, with each subsequent term increasing by 3/8. Since the constant difference is 3/8, the sequence is arithmetic with a fixed increment of 3/8 between each term. Now, looking at the statements: 1. “The sequence is recursive, where each term is 1/4 greater than its preceding term.” - Incorrect because the increase is 3/8, not 1/4. 2. “The sequence is recursive and can be represented by the function f(n+1)=f(n)+3/8.” - Correct, as each term is indeed 3/8 greater than the prior term. 3. “The sequence is arithmetic, where each pair of terms has a constant difference of 3/4.” - Incorrect because the constant difference is not 3/4 but 3/8. 4. “The sequence is arithmetic and can be represented by the function f(n+1)=f(n)(3/8).” - Incorrect because this implies a multiplicative relationship, which does not apply here. Thus, the correct description of the sequence is the second statement.