In order to have a linear equation, you have to write an equation like
[tex]y=mx+q[/tex]
The sequence has to start with 3, so we must choose [tex]q=3[/tex], because this guarantees that when [tex]x=0[/tex] we have
[tex]y=0\cdot m + 3 =3[/tex]
Now, [tex]m[/tex] must be even. In fact, if [tex]m[/tex] is even, [tex]mx[/tex] will always be even for every possible [tex]x[/tex], and [tex]mx+3[/tex] will be odd.
So, for example, you might choose
[tex]y=2x+3[/tex]
Which will produce the following sequence:
[tex]\begin{array}{c|c}x&f(x)\\0&3\\1&5\\2&7\\3&9\end{array}[/tex]
and so on
