To complete the recursive formula for \( g(n) \), we start from the given function:
\[ g(n) = 25 - 49(n - 1) \]
First, we will calculate \( g(1) \) to find the base case of the recursion:
\[ g(1) = 25 - 49(1 - 1) = 25 - 49(0) = 25 - 0 = 25 \]
Now, we need to express \( g(n) \) in terms of \( g(n-1) \). Let's compute \( g(n-1) \):
\[ g(n-1) = 25 - 49((n-1) - 1) = 25 - 49(n - 2) = 25 - 49n + 98 = 123 - 49n \]
Now we will rewrite \( g(n) \) in terms of \( g(n-1) \):
\[ g(n) = 25 - 49(n - 1) = 25 - 49n + 49 = 74 - 49n \]
Next, we express the difference \( g(n) - g(n-1) \):
\[ g(n) - g(n-1) = (74 - 49n) - (123 - 49n) = 74 - 49n - 123 + 49n = 74 - 123 = -49 \]
So we can establish the recursive relationship:
\[ g(n) = g(n-1) - 49 \]
Putting everything together, we have:
\[ \begin{align*} g(1) &= 25 \ g(n) &= g(n-1) - 49 \quad \text{for } n > 1 \end{align*} \]
Thus, the completed recursive formula is:
\[ g(1) = 25 \] \[ g(n) = g(n-1) - 49 \quad \text{for } n > 1 \]