Looks like you just evaluated the summand for the given value of [tex]n[/tex], whereas the question is asking you to find the value of the sum for the first [tex]n[/tex] terms.
Let [tex]S_k=\displaystyle\sum_{n=1}^k\frac3{(-2)^n}[/tex]. Then [tex]S_k[/tex] is the [tex]k[/tex]th partial sum.
[tex]S_1[/tex] happens to be the first term in the series, which is why that box is marked correct:
[tex]S_1=\displaystyle\sum_{n=1}^1\frac3{(-2)^n}=\frac3{(-2)^1}=-1.5[/tex]
But the next partial sum is not correct:
[tex]S_2=\displaystyle\sum_{n=1}^2\frac3{(-2)^n}=\frac3{(-2)^1}+\frac3{(-2)^2}=-0.75[/tex]
and this is not the same notion as the second term (which indeed is 0.75) in the series.
