an atirmetic sequence can be written in form
[tex]a_n=a_1+d(n-1)[/tex]
where [tex]a_n[/tex] is the nth term
[tex]a_1[/tex] is the first term
[tex]d[/tex] is the common difference
[tex]n[/tex] is the counter variable
so, given that first term is 14 ([tex]a_1=14[/tex]) and given taht 25th term is 206 ([tex]a_{25}=206[/tex]), we want to find d
[tex]a_{25}=206[/tex]
[tex]a_{25}=a_1+d(25-1)[/tex]
[tex]206=14+24d[/tex]
minus 14 both sides
[tex]192=24d[/tex]
divide both sides by 24
[tex]8=d[/tex]
the common difference is 8
