The nth term of the sequence -2, 1, 4, 7, is given by the formula a) an = n - 3 b) an = 3n - 3 c) an = n - 5 d) an = 3n - 5

First we need to find what kind of sequence we have. To do that we are going to test if the sequence as a difference , in which case it will be an arithmetic sequence, or a ratio , in which case it will be geometric sequence.
The formula to find  is 
where 
is the current term in the sequence
is the previous term in the sequence 
The formula to find  is 
where 
is the current term in the sequence 
is the previous term in the sequence 
- For  and 
  
  
  
- For  and :
  
  
  
  
Since  is equal in both procedures whereas is not, we can conclude that our sequence is an arithmetic sequence.
Now we are going to use the explicit formula of an arithmetic sequence 
where 
is the nth term
is the first term 
is the position of the term in the sequence 
is the difference 
We know that  and , so lets replace those values in our formula:




We can conclude that the correct answer is D)an = 3n - 5