Notice that the sequence has a common ratio. To find it, divide the 2nd term over the 1st term:
[tex]r=\frac{-36}{-9}=4[/tex]
Verify that the same ratio is hold on the next terms:
[tex]\begin{gathered} r=\frac{-144}{-36}=4 \\ r=\frac{-576}{-144}=4 \end{gathered}[/tex]
The explicit formula for the nth term of a sequence with first term a and common ratio r is:
[tex]a_n=a\cdot r^{n-1}[/tex]
Then, the explicit formula for this sequence is:
[tex]a_n=-9\times4^{n-1}[/tex]
Since each term of the sequence is 4 times the previous term, then the recursive formula for this sequence, is:
[tex]\begin{gathered} a_n=4\cdot a_{n-1} \\ a_1=-9 \end{gathered}[/tex]
