the givn is 3 -6 12 -24 find the sequence equation

Each number is -2 times the previous. So you know it'll be something like

A_n=c \cdot (-2)^n,

where A_n is the nth term and c is some constant that you have to figure out. It's simple enough to figure out what c is: just plug in the values for the first number.

3=c \cdot (-2)^1

\frac{3}{-2^1}=c

c=-\frac{3}{2}

So

A_n=-\frac{3}{2} \cdot (-2)^n

or to simplify a little more

A_n=3 \cdot \frac{(-2)^n}{-2}

A_n=3 \cdot (-2)^{n-1}

It is rather obvious that the numbers are multiples of 3.

Try 3\cdot (-2)^{n}, \;\ n=0,1,2......

What's the next number?