Answer:
[tex]a_n=11-10\,n[/tex]
Step-by-step explanation:
Notice that in the sequence :
1, -9, -19, ... one term differs from the following by a constant number that is subtracted from the first one. There is what is called a "common difference" (d = -10)
the first term is "1", and we can apply the formula for the nth term of an arithmetic sequence for which we know the first term , and the common difference:
[tex]a_n=a_1+(n-1) * d\\a_n=1\,+\,(n-1)*(-10)\\a_n=1-10\,n+\,10\\a_n=11-10\,n[/tex]
