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{f(1)=2, f(2)=5, f(n)=f(n2)f(n1)\begin{cases} f(1) = -2, \ f(2) = 5, \ f(n) = f(n-2) \cdot f(n-1) \end{cases}, f(3)=0f(3) = \boxed{\phantom{0}}

Full solution

Q. {f(1)=2, f(2)=5, f(n)=f(n2)f(n1)\begin{cases} f(1) = -2, \ f(2) = 5, \ f(n) = f(n-2) \cdot f(n-1) \end{cases}, f(3)=0f(3) = \boxed{\phantom{0}}
  1. Identify Values: Identify the values of f(1)f(1) and f(2)f(2).f(1)=2f(1) = -2 and f(2)=5f(2) = 5.
  2. Use Recursive Formula: Use the recursive formula to find f(3)f(3).f(3)=f(1)×f(2)=(2)×5=10f(3) = f(1) \times f(2) = (-2) \times 5 = -10.