What is the nth term of - 4,-3,0,5,12,21,32?

The first set of differences is 1,3,5,7,9,11

second set of difference = 2 so this is a quadratic sequence with first term n^2

subtract n^2 from the sequence:-

-4 - 3 0 5

1 4 9 16

-5 - 7 - 9 - 11

This last series is an AP with nth term = - 5-2 (n - 1)

so nth term for original series is n^2 - 5 - 2 (n - 1)

= n^2 - 2n - 3 answer