Question

Nth term of -4 ,1, 12 ,29, 52

Answer 1

`3n^2-4n-3`

Explanation:

The difference between each number is 5,11,17,23 and the difference between these numbers is 6. So by dividing 6 by 2, you get the n^2 co-efficient which in this case is
`3n^2`.

Then compare the
`3n^2\\` pattern to the original pattern so:

-4, 1, 12, 29, 52

3, 12, 27, 48, 75

Subtract the original nth term sequence by the new
`3n^2\\` pattern and you will get:

-7, -11, -15, -19, -23

The nth term of this new sequence is -4n-3.

By combining the 2 nth terms together, you get
`3n^2-4n-3`.

Hope this helps!