Answer:
[tex]a_n=-2\cdot 9^{n-1}.[/tex]
Step-by-step explanation:
You are given that
- [tex]a_1=-2;[/tex]
- [tex]a_n=9a_{n-1}.[/tex]
Then
[tex]a_1=-2,\\ \\a_2=9a_1=9\cdot (-2)=-18,\\ \\a_3=9a_2=9\cdot (-18)=-162, \dots[/tex]
Actually, this sequence is the geometric seequence with first term [tex]a_1=-2[/tex] and ratio [tex]r=9.[/tex]
The explicit rule for the nth term of the geometric sequence is
[tex]a_n=a_1\cdot r^{n-1}.[/tex]
Hence,
[tex]a_n=-2\cdot 9^{n-1}.[/tex]
