The rule of an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_1[/tex] - first term
[tex]d[/tex] - a difference [tex]d=a_n-a_{n-1}[/tex]
We have:
[tex]a_1=20;\ a_2=17;\ a_3=14;\ a_4=11;\ a_5=8;\ ...[/tex]
[tex]a_1=20;\ d=a_2-a_1\to d=17-20=-3[/tex]
substitute:
[tex]a_n=20+(n-1)\cdot(-3)=20-3n+3=-3n+23[/tex]
Answer: f(n) = -3n + 23
