Let x-2, 4x, 7x+2 be three first terms of arithmetical sequence. Then
[tex]a_1=x-2, \\ a_2=4x, \\ a_3=7x+2[/tex].
Since [tex]d=a_2-a_1=a_3-a_2[/tex], you receive that [tex]d=4x-(x-2)=7x+2-4x=3x+2[/tex].
The formula for n-th term of arithmetical sequence is:
[tex]a_n=a_1+(n-1)d[/tex].
Hence [tex]a_{12}=a_1+11d=x-2+11(3x+2)=x-2+33x+22=34x+20[/tex].
