Answer:
The nth term = n^2 - 2n - 3.
Step-by-step explanation:
-4 -3 0 5 12 21 32
Differences 1 3 5 7 9 11
Difference 2 2 2 2 2 <-- divide this by 2 so its n^2.
So the first term is n^2
List the original numbers and values of n^2:
sequence -4 -3 0 5 12 21 32
n^2 1 4 9 16 25 36 49
Subtract -5 -7 -9 -11 -13 -15 -17
These last numbers have a common difference of -2 so the next part of the answer is -2n and get the -5, -7 etc we add -3.
So our formula is n^2 - 2n - 3.
Check for the 3rd term:
3rd term is 3^2 - 2(3) - 3 = 0.
5th term = 5^2 - 2(5) - 3 = 25 - 10 - 3 = 12.
