Find the formula for the nth
term of the following quadratic sequence, as an expression in
n:
4,14,28,46,…

2n^2 + n - 2.

Step-by-step explanation:

n:                            1     2       3      4

Term:                     4     14    28   46

Common Diff           10    14    18

2nd Diff                        4      4            - So the formula will contain 2n^2

2n^2                      2     8       18    32

Term:                     4    14      28    46

term-2n^2:             2     6       10    14

The last set is an arithmetic sequence with nth term = 2 + (n -1)*4 = n - 2.

So the formula is 2n^2 + ( n - 2)