Answer:
[tex]3n^2-4n-3[/tex]
Step-by-step 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 [tex]3n^2[/tex].
Then compare the [tex]3n^2\\[/tex] 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 [tex]3n^2\\[/tex] 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 [tex]3n^2-4n-3[/tex].
Hope this helps!
