Chapter 11 - Section 11.4 - Partial Sums of Arithmetic and Geometric Sequences - Exercise Set - Page 658: 8

$S_4=\dfrac{11}{3}$

Using $S_n=\dfrac{a_1(1-r^n)}{1-r}$, the sum of the first $ 5 $ terms of the sequence $ \dfrac{1}{3},-\dfrac{2}{3},\dfrac{4}{3},... $ is \begin{array}{l} S_4=\dfrac{\dfrac{1}{3}\left(1-(-2)^5\right)}{1-(-2)}\\\\ S_4=\dfrac{\dfrac{1}{3}(33)}{3}\\\\ S_4=\dfrac{11}{3} .\end{array}