ANSWER
\(f(5)=7.5\)
EXPLANATION
The recursive definition is
\(f(n+1)=-0.5f(n)\).
Since the first term of the sequence is given to us, we need to plug in \(n=1\).
This implies that;
\(f(1+1)=-0.5f(1)\).
\(f(2)=-0.5f(1)\)
But we were given that, \(f(1)=120\).
This implies that;
\(f(2)=-0.5\times 120\)
\(f(2)=-60\)
Since we now know that \(f(2)=-60\), we again plug in \(n=2\) in to the recursive definition.
\(f(2+1)=-0.5f(2)\)
\(\Righarrow f(3)=-0.5\times -60\)
\(\Righarrow f(3)=30\).
We plug \(n=3\) in to the formula again to determine the 4th term.
\(f(4)=-0.5f(3)\).
\(f(4)=-0.5 \times 30\)
\(f(4)=-15\).
We finally find the 5th term by substituting \(n=4\).
\(f(4+1)=-0.5f(4)\)
\(f(5)=-0.5\times (-15)\)
\(f(5)=7.5\)
