You can see that each term is twice the previous one, with inverted sign.
You double a number by multiplying it by two, and you change its sign by multiplying it by -1.
So, you multiply each term by 2 and by -1, which results in a multiplication by -2.
Since we start with 3, the terms are
[tex]a_1 = 3[/tex]
[tex]a_2 = 3\cdot (-2) = -6[/tex]
[tex]a_3 = -6\cdot (-2) = 12[/tex]
and so on. So, the general term is
[tex]a_n = 3\cdot(-2)^{n-1}[/tex]
