To find an explicit formula for the function \( h(n) \), we can analyze the given recursion.
We start with the initial condition:
\[ h(1) = 96 \]
And the recursive definition:
\[ h(n) = h(n - 1) - 1 \quad \text{for } n > 1 \]
Let's calculate the first few terms to see the pattern:
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For \( n = 1 \): \[ h(1) = 96 \]
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For \( n = 2 \): \[ h(2) = h(1) - 1 = 96 - 1 = 95 \]
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For \( n = 3 \): \[ h(3) = h(2) - 1 = 95 - 1 = 94 \]
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For \( n = 4 \): \[ h(4) = h(3) - 1 = 94 - 1 = 93 \]
From these calculations, we can see that as \( n \) increases by 1, \( h(n) \) decreases by 1. This gives us a linear pattern.
To find a general formula, we note that \( h(n) \) decreases by 1 for each increment of \( n \). Therefore, for any \( n \), we can express \( h(n) \) in terms of \( h(1) \):
\[ h(n) = h(1) - (n - 1) \]
Substituting \( h(1) = 96 \):
\[ h(n) = 96 - (n - 1) \]
This simplifies to:
\[ h(n) = 96 - n + 1 \]
So,
\[ h(n) = 97 - n \]
Thus, the explicit formula for \( h(n) \) is:
\[ \boxed{97 - n} \]