# A pendulum Makes an arc of length of 18 in. on its first swing. On Each suceeding Swing,The length of the arc is one-third the lenght of the preceding swing.How far does the Tip of the pendulum move before it comes to rest?

## Infinite Geometric Sequence

$= 18 \left(1 + \frac{1}{3} + \frac{1}{3} ^ 2 + \frac{1}{3} ^ 3. \ldots . \text{up to } \infty\right)$ in.
$= 18 \cdot \left(\frac{1}{1 - \frac{1}{3}}\right)$ in
$= 18 \cdot \frac{3}{2} = 27$ in.