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