Answer :
Let's analyze the sequence and determine the recursive function.
1. The given sequence is
$$14,\; 24,\; 34,\; 44,\; 54,\; \ldots$$
2. In an arithmetic sequence, the common difference is the difference between any two consecutive terms. We calculate it by subtracting the first term from the second term:
$$\text{Common difference} = 24 - 14 = 10.$$
3. For an arithmetic sequence, the recursive function is defined by
$$f(n+1) = f(n) + \text{common difference},$$
with the initial term $f(1)$ given.
4. Since the common difference is $10$ and the first term $f(1)$ is $14$, the recursive function is:
$$f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14.$$
Thus, the statement that describes the recursive function used to generate the sequence is:
$$\text{"The common difference is 10, so the function is } f(n+1)=f(n)+10 \text{ where } f(1)=14."$$
1. The given sequence is
$$14,\; 24,\; 34,\; 44,\; 54,\; \ldots$$
2. In an arithmetic sequence, the common difference is the difference between any two consecutive terms. We calculate it by subtracting the first term from the second term:
$$\text{Common difference} = 24 - 14 = 10.$$
3. For an arithmetic sequence, the recursive function is defined by
$$f(n+1) = f(n) + \text{common difference},$$
with the initial term $f(1)$ given.
4. Since the common difference is $10$ and the first term $f(1)$ is $14$, the recursive function is:
$$f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14.$$
Thus, the statement that describes the recursive function used to generate the sequence is:
$$\text{"The common difference is 10, so the function is } f(n+1)=f(n)+10 \text{ where } f(1)=14."$$
