Answer
$S_{1}=3;$
$S_{2}=S_{1}-\dfrac {9}{2}=-\dfrac {3}{2};$
$S_{3}=S_{2}+\dfrac {27}{4}=\dfrac {21}{4};$
$S_{4}=S_{3}-\dfrac {81}{8}=-\dfrac {39}{8};$
$S_{5}=S_{4}+\dfrac {243}{16}=\dfrac {165}{16}$
Work Step by Step
$S_{n}=3-\dfrac {9}{2}+\dfrac {27}{4}-\dfrac {81}{8}+\dfrac {243}{16}\ldots $
$S_{1}=3;$
$S_{2}=S_{1}-\dfrac {9}{2}=-\dfrac {3}{2};$
$S_{3}=S_{2}+\dfrac {27}{4}=\dfrac {21}{4};$
$S_{4}=S_{3}-\dfrac {81}{8}=-\dfrac {39}{8};$
$S_{5}=S_{4}+\dfrac {243}{16}=\dfrac {165}{16}$
