Answer:
The seventh term in the sequence is -729.
Step-by-step explanation:
Notice that the sequence is not increasing linearly. Therefore, this is a geometric sequence.
Recall that the explicit formula for a geometric sequence is given by:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the first term, r is the common ratio, and n denotes the nth term.
From the sequence, we can see that our first term a is -1.
Because each term is thrice the previous, our common ratio r is 3.
By substitution:
[tex]x_n=-(3)^{n-1}[/tex]
Hence, the seventh term is:
[tex]\displaystyle \begin{aligned} x_7 & = -(3)^{(7)-1} \\ \\ & = -(3)^{6} \\ \\ & = -729\end{aligned}[/tex]
In conclusion, the seventh term is -729.
