\(a_n=a_1+d(n-1)\) 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
\(a_6=a_1+6(6-1)=22\)
\(a_1+6(5)=22\)
\(a_1+30=22\)
minus 30 both sides
\(a_1=-8\)
so
the formula is
\(a_n=-8+6(n-1)\)
the 50th term is subsitute 50 for n
\(a_{50}=-8+6(50-1)\)
\(a_{50}=-8+6(49)\)
\(a_{50}=-8+294\)
\(a_{50}=286\)
the 50th term is 286
