[tex]a_{1} = 10[/tex]
[tex]a_{4} = 19[/tex]
[tex]a_{2} = a_{1} + r[/tex]
[tex]a_{3} = a_{2} + r = a_{1} + r + r = a_{1} + 2r[/tex]
[tex]a_{4} = a_{3} + r = a_{1} + 2r + r = a_{1} + 3r[/tex]
[tex]a_{4} = a_{1} + 3r[/tex]
[tex]19 = 10 + 3r[/tex]
[tex]3r = 19 - 10[/tex]
[tex]3r = 9 \: | \div 3[/tex]
[tex]r = 3[/tex]