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{[f(1)=15],[f(n)=f(n-1)*n]:} f(2)=

{f(1)=15f(n)=f(n−1)⋅nf(2)=□ \begin{array}{l}\left\{\begin{array}{l}f(1)=15 \\ f(n)=f(n-1) \cdot n\end{array}\right. \\ f(2)=\square\end{array}

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Full solution

Q. {f(1)=15f(n)=f(n−1)⋅nf(2)=□ \begin{array}{l}\left\{\begin{array}{l}f(1)=15 \\ f(n)=f(n-1) \cdot n\end{array}\right. \\ f(2)=\square\end{array}
  1. Problem Prompt: The question prompt asks us to find the value of f(2)f(2) given the recursive function f(n)=f(n−1)⋅nf(n) = f(n-1) \cdot n with the initial condition f(1)=15f(1) = 15.
  2. Initial Condition: We know that f(1)=15f(1) = 15. To find f(2)f(2), we use the recursive formula f(n)=f(n−1)⋅nf(n) = f(n-1) \cdot n with n=2n = 2.
  3. Recursive Formula: Substitute n=2n = 2 into the recursive formula to get f(2)=f(2−1)×2f(2) = f(2-1) \times 2.
  4. Substitute n=2 n = 2 : Calculate f(2) f(2) using the known value of f(1) f(1) : f(2)=f(1)×2=15×2 f(2) = f(1) \times 2 = 15 \times 2 .
  5. Calculate f(2)f(2): Perform the multiplication to find f(2)f(2): f(2)=30f(2) = 30.

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