Answer
The common ratio is -3 so yes, this is a geometric sequence.
The explicit formula is $a_{n}$=3$\times$ $(-3)^{n-1}$.
The recursive formula is $a_{1}$=3;$a_{n}$=$a_{n-1}$ $\times$ -3
Work Step by Step
You are given the sequence 3,-9,27,-81.The starting value $a_{1}$=3.Find the common ratio by using the formula: R=$\frac{a2}{a1}$,R=$\frac{a4}{a3}$.Plug in the values to get the ratio:
r=$\frac{-9}{3}$=-3
r=$\frac{-81}{27}$=-3
There is a common ratio, r=-3. So the sequence is geometric.
Substitute a1 and R into the explicit formula($a_{n}$=$a_{1}$ $\times$$r^{n-1}$).The explicit formula is $a_{n}$=3$\times$ $(-3)^{n-1}$.
Substitute a1 and r into the recursive formula ($a_{1}$=A;$a_{n}$=$a_{n-1}$$\times$R). The recursive formula is $a_{1}$=3; $a_{n}$=$a_{n-1}$ $\times$ -3
