Answer
$134.08$ inches
Work Step by Step
$16,0.96(16), (0.96)^{2}(16),...$
First term $a_{1}= 16$ and common ratio $r = 0.96$
Sum of the first $n$ terms of Geometric sequence is
$S_{n}= \frac{a_{1}(1-r^{n})}{1-r}$
Substituting $a_{1}= 16, r = 0.96$ and $n=10$
$S_{10}= \frac{16(1-(0.96)^{10})}{1-0.96}$
$S_{10}= \frac{16(1-0.6648)}{1-0.96}$
$S_{10}= \frac{16(0.3352)}{0.04}$
$S_{10}= 134.08$
The total length of the distance the pendulum has swung, after 10 swings is $134.08$ inches
