What is the nth term rule of the quadratic sequence below / -7, - 4, 3, 14, 29, 48, 71

nth term = 2n^2 - 3n - 6.

Step-by-step explanation:

n = 1 2 3 4 5 6 7

- 7 - 4 3 14 29 48 71

Differences 3 7 11 15 19 23

Differences 4 4 4 4 4

So the first term in the Rule is 2n^2

Subtracting the values of 2n^2 from the original terms:

- 7 - 4 3 14 29 48 71

2n^2 2 8 18 32 50 72 98

Subtrct - 9 - 12 - 15 - 18 - 21 - 24 - 27

-3 - 3 - 3 - 3 - 3 - 3

So we have - 3n and the last term is - 6 because - 7 = 2 (1) ^2 - 3 - 6 and the other terms fit this pattern as well.