Question

What is the formula for the following arithmetic sequence? -9 , -2 , 5 , 12

Answer 1

You add 7 to get the next number in the sequence:
-9 + 7 = -2; -2 + 7 = 5; 5 + 7 = 12; and so on.

Answer 2

First term:  -9
Common difference:  7


a(n) = -9 + 7(n-1), for n = {1, 2, 3, ... }

Check:  what is the first term?  let n=1.   Then a(1) = -9 + 7(1-1) = -9.  
This is correct.