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Sagot :
To solve for \( f(2) \) given the recurrence relation:
[tex]\[ \begin{array}{l} f(1) = -3 \\ f(n) = -5 \cdot f(n-1) - 7 \end{array} \][/tex]
we need to follow these steps:
1. Identify the value of \( f(1) \):
[tex]\[ f(1) = -3 \][/tex]
2. Use the recurrence relation to find \( f(2) \):
[tex]\[ f(2) = -5 \cdot f(1) - 7 \][/tex]
3. Substitute the value of \( f(1) \) into the equation for \( f(2) \):
[tex]\[ f(2) = -5 \cdot (-3) - 7 \][/tex]
4. Simplify the multiplication:
[tex]\[ f(2) = 15 - 7 \][/tex]
5. Perform the subtraction:
[tex]\[ f(2) = 8 \][/tex]
Thus, the value of \( f(2) \) is:
[tex]\[ f(2) = 8 \][/tex]
[tex]\[ \begin{array}{l} f(1) = -3 \\ f(n) = -5 \cdot f(n-1) - 7 \end{array} \][/tex]
we need to follow these steps:
1. Identify the value of \( f(1) \):
[tex]\[ f(1) = -3 \][/tex]
2. Use the recurrence relation to find \( f(2) \):
[tex]\[ f(2) = -5 \cdot f(1) - 7 \][/tex]
3. Substitute the value of \( f(1) \) into the equation for \( f(2) \):
[tex]\[ f(2) = -5 \cdot (-3) - 7 \][/tex]
4. Simplify the multiplication:
[tex]\[ f(2) = 15 - 7 \][/tex]
5. Perform the subtraction:
[tex]\[ f(2) = 8 \][/tex]
Thus, the value of \( f(2) \) is:
[tex]\[ f(2) = 8 \][/tex]
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