In this question we have numbers that create a geometric sequence, where each number is the previous one multiplied by a common ratio.
In order to find this ratio, we just need to divide one term by the previous term:
[tex]\text{ratio}=-\frac{12}{3}=-4[/tex]Now, to find the 7th term, we can use the formula:
[tex]a_n=a_1\cdot q^{n-1}[/tex]Where a1 is the first term and q is the common ratio. Using n = 7, we have:
[tex]\begin{gathered} a_7=3\cdot(-4)^6 \\ a_7=3\cdot4096 \\ a_7=12288 \end{gathered}[/tex]So the 7th term of this sequence is 12,288.
