1/4 = 3/12, and 5/4 = 15/12, so it looks like there's a common difference between terms of 4/12 = 1/3. The the [tex]n[/tex]-th term in the sequence is given recursively by
[tex]\begin{cases}a_1=\frac14\\a_n=a_{n-1}+\frac13&\text{for }n>1\end{cases}[/tex]
By substitution, we get
[tex]a_n=a_{n-1}+\dfrac13\implies a_n=\left(a_{n-2}+\dfrac13\right)+\dfrac13[/tex]
[tex]a_n=a_{n-2}+\dfrac23[/tex]
and doing this again and again until we stop with an expression containing [tex]a_1[/tex], we find that
[tex]a_n=a_1+\dfrac{n-1}3[/tex]
[tex]a_n=\dfrac{4n-1}{12}[/tex]
Then the 12th term in the sequence is
[tex]a_{12}=\dfrac{4\cdot12-1}{12}=\boxed{\dfrac{47}{12}}[/tex]
