Answer:
The sequence has common difference 3, and its general nth term can be written as:
[tex]a_n=3\,n-1[/tex]
Step-by-step explanation:
In order to define the sequence, we recall the formula for the nth term of an arithmetic sequence as:
[tex]a_n=a_1+(n-1)\,d[/tex]
where "d" is the common difference for the sequence (our unknown in this case), and the nth term is our fourth term (n = 4) which equals 11, and the first term is 2:
[tex]a_n=a_1+(n-1)\,d\\11=2+(4-1)\,d\\9=3\,d\\d=9/3\\d=3[/tex]
Therefore our sequence has common difference 3, and its general nth term can be written as:
[tex]a_n=2+(n-1)3\\a_n=3\,n-1[/tex]
