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{[f(1)=-16],[f(n)=-29-f(n-1)]:}

f(2)=

$\begin{array}{l}\left\{\begin{array}{l}f(1)=-16 \\ f(n)=-29-f(n-1)\end{array}\right. \\ f(2)=\square\end{array}$

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Evaluate recursive formulas for sequences

Full solution

Q.

\begin{array}{l}\left\{\begin{array}{l}f(1)=-16 \\ f(n)=-29-f(n-1)\end{array}\right. \\ f(2)=\square\end{array}

Given function and value: We are given the function f(n) and its value at n= $1$ : $\newline$ $f(1) = -16$ $\newline$ $f(n) = -29 - f(n-1)$ $\newline$ To find f( $2$ ), we need to substitute n= $2$ into the second equation.
Substituting n= $2$ : Substituting n= $2$ into the function, we get: $\newline$ $f(2) = -29 - f(2-1)$ $\newline$ $f(2) = -29 - f(1)$ $\newline$ Now we can substitute the value of f( $1$ ) into this equation.
Substituting f( $1$ ): Using the value of f( $1$ ) which is $-16$ , we substitute it into the equation for f( $2$ ): $\newline$ $f(2) = -29 - (-16)$ $\newline$ $f(2) = -29 + 16$ $\newline$ Now we perform the arithmetic operation to find the value of f( $2$ ).
Calculating f( $2$ ): Calculating the value of f( $2$ ): $\newline$ $f(2) = -29 + 16$ $\newline$ $f(2) = -13$ $\newline$ We have found the value of f( $2$ ).

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