Consider a geometric sequence [tex](u_n)[/tex]
let [tex]u_1=a[/tex] and the common ratio be r, then the sequence is constructed as follows:
[tex]u_1, u_2, u_3..... = a, ar, a r^{2}, a r^{3}, ...[/tex]
we can observe that each term of the sequence is its previous term * r.
In the given sequence, to find the common ratio we divide 6,561 by −2,187 and get -3. This means that [tex]r= -\frac{1}{3} [/tex]
Let the first term [tex]u_1=a=6,561[/tex],
then the eighth term is
[tex]u_8=a* r^{7}= 6,561 (- \frac{1}{3} )^{7}= -6,561*( \frac{1}{3} )^{7}= \frac{-6,561}{2187} =-3[/tex]
Answer: -3
