To find the height of the ball the 5th time it goes up the cylinder we just need to plug n=5 in the expression given:
[tex]\begin{gathered} a_5=8(\frac{1}{2})^{5-1} \\ a_5=8(\frac{1}{2})^4 \\ a_5=\frac{1}{2} \end{gathered}[/tex]
Therefore, the height the ball reaches the 5th time it goes up is 1/2 inches (or 0.5 inches in decimal form)
