Given the series:
3 - 12 + 48 - 192 + ...
It can be identified as a geometric series because the common ratio is constant:
[tex]r=\frac{-12}{3}=-4[/tex]Now calculate the following terms:
a5 = (-192) * (-4) = 768
a6 = 768 * (-4) = -3072
a7 = -3072 * (-4) = 12288
a8 = 12288 * (-4) = -49152
The sum of the first eight terms is:
3 - 12 + 48 - 192 + 768 - 3072 + 12288 - 49152 = -39321
Sum = -39321