Answer
The series converges and the sum is -2
See graph
Work Step by Step
$a_{n}= \frac{12}{(-5)^{n}}$
partial sum: $s_{n}=a_{1}+a_{2}...+ a_{n}$
$n=1$ $a_{1}=-2.4$ $s_{1}=-2.4$
$n=2$ $a_{2}= 0.48$ $s_{2}=-1.92$
$n=3$ $a_{3}=-0.096$ $s_{3}=-2.016$
$n=4$ $a_{4}=0.0192$ $s_{4}=-1.9968$
$n=5$ $a_{5}=-0.00384$ $s_{5}=-2.00064$
$n=6$ $a_{6}= 7.68 \times 10^{-4}$ $s_{6}= -1.999872$
$n=7$ $a_{7}= -1.536 \times 10^{-4}$ $s_{7}= -2.0000256$
The partial sum appears to be converging to -2
$\Sigma^{\infty}_{n=1} \frac{12}{(-5)^{n}}$
$a = -\frac{12}{5}$ and common ratio as $r= -\frac{1}{5}$
Series converges because $|r|=\frac{1}{5} \lt 1$
Sum of series is given by
$\frac{a}{1-r}$
$=\frac{-\frac{12}{5}}{1-(-\frac{1}{5})}$
$= \frac{-\frac{12}{5}}{1+\frac{1}{5}}$
$= \frac{-\frac{12}{5}}{\frac{6}{5}}$
$=-2$
