# Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.3 - Page 741: 76

$134.08$ 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

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