Question

The sixth term is 22 and the difference is six what is the fiftieth term?

Answer 1

$a_n=a_1+d(n-1)$ 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