According to the given sequence, the difference is -4, because it's decreasing with that difference: 2-2 = -2; -2-4 = -6; and so on.
To find the explicit formula, we use the arithmetic sequence formula.
[tex]a_n=a_1+(n-1)d[/tex]Replacing all the given information, we have.
[tex]\begin{gathered} a_n=2+(n-1)\cdot(-4) \\ a_n=2-4n+4 \\ a_n=6-4n \end{gathered}[/tex]This explicit formula we can also express as
[tex]f(n)=6-4n[/tex]