We find the first differences between terms: 7-4=3; 12-7=5; 19-12=7; 28-19=9. Since these are different, this is not linear. We now find the second differences: 5-3=2; 7-5=2; 9-7=2. Then:
Since these are the same, this sequence is quadratic. We use (1/2a)n², where a is the second difference: (1/2*2)n²=1n².
We now use the term number of each term for n: 4 is the 1st term; 1*1²=1. 7 is the 2nd term; 1*2²=4. 12 is the 3rd term; 1*3²=9. 19 is the 4th term; 1*4²=16. 28 is the 5th term: 1*5²=25.
Now we find the difference between the actual terms of the sequence and the numbers we just found:
4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.
Since this is constant, the sequence is in the form (1/2a)n²+d; in our case, 1n²+d, and since d=3, 1n²+3. The correct answer is n²+3
