[tex]T_n = a_1+ d(n-1) [/tex]
Given that d = 6 and 6th term is 22,
[tex]22 = a_1+ 6(6-1) [/tex]
[tex]22 = a_1+ 30[/tex]
[tex]a_1 = 22- 30[/tex]
[tex]a_1 = -8[/tex]
So the general equation is
[tex]T_n = -8 + 6(n-1)[/tex]
[tex]T_n = -8 + 6n-6[/tex]
[tex]T_n =6n-14[/tex]
When n = 15,
[tex]T_{15} = 6(15)-14[/tex]
[tex]T_{15} = 136[/tex]
Answer: 136
