Chapter 7 - Section 7.3 - Geometric Sequences and Series - 7.3 Exercises - Page 654: 26

$S_5=-14.8243080631\approx -14.82$

In a geometric series the ratio between consecutive terms is constant. The $S_n$, so the sum of the first n terms can be written as: $S_n=a_1\times \frac{1-r^{n}}{1-r}$ Here, $n=5$, $a_1=-3.772$, $r=-1.553$: $S_n=a_1\times \frac{1-r^{n}}{1-r}$ $S_5=-3.772\times \frac{1-(-1.553^{5})}{1-(-1.553)}=-14.8243080631\approx -14.82$