Question

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

Answer 1

Answer:

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.