Let [tex]a_n[/tex] denote the [tex]n[/tex]-th term in the sequence. For an arithmetic sequence, there is a constant number added to successive terms:
[tex]a_7=a_6+d[/tex]
[tex]a_8=a_7+d=a_6+2d[/tex]
[tex]a_9=a_8+d=a_6+3d[/tex]
[tex]\cdots[/tex]
[tex]a_{12}=a_{11}+d=a_6+6d[/tex]
We know [tex]a_6=\dfrac32[/tex] and [tex]a_{12}=\dfrac52[/tex], so we get
[tex]\dfrac52=\dfrac32+6d\implies 6d=1\implies d=\dfrac16[/tex]
