Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:
[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]
Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:
[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]
Then substitute f(3) down to f(1):
[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]
Therefore, f(5) = 7.5