Question

Find the formula for the

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

Answer 1

2n^2 + n - 2.

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)