[tex]a_n=a_1+d(n-1)[/tex] is the formula for an arithmetic sequence
an=nth term
a1=first term
d=common difference
n=which one it is
given
6th term or a6 is 22
and d or common differece is 6 then
[tex]a_6=a_1+6(6-1)=22[/tex]
[tex]a_1+6(5)=22[/tex]
[tex]a_1+30=22[/tex]
minus 30 both sides
[tex]a_1=-8[/tex]
so
the formula is
[tex]a_n=-8+6(n-1)[/tex]
the 50th term is subsitute 50 for n
[tex]a_{50}=-8+6(50-1)[/tex]
[tex]a_{50}=-8+6(49)[/tex]
[tex]a_{50}=-8+294[/tex]
[tex]a_{50}=286[/tex]
the 50th term is 286
