Solution:
The series is given below as
[tex]-3+(1.2)+(-0.48)+.....[/tex]
Step 1:
We will calculate the common ratio
[tex]\begin{gathered} r=\frac{a_2}{a_1}=\frac{a_3}{a_2} \\ r=\frac{1.2}{-3}=-\frac{0.48}{1.2} \\ r=-0.4 \end{gathered}[/tex]
The sum of infinite series will be calculated using the formula below
[tex]\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ S_{\infty}=-\frac{3}{1-(-0.4)} \\ S_{\infty}=-\frac{3}{1+0.4} \\ S_{\infty}=-\frac{3}{1.4} \\ S_{\infty}=-3\times\frac{10}{14} \\ S_{\infty}=-\frac{30}{14} \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow-\frac{30}{14}[/tex]
