Question

Find an expression for the number in the nth term pattern of the sequence.
4 , 7 , 12, 19

Answer 1

n^2 + 3.

Explanation:

4 7 12 19

Differences are 3 5 7 so this a quadratic sequence.

2nd difference = 2 2

So the first part of the expression is n^2

Terms: 4 7 12 19

n^2 1 4 9 16

Difference = 3 3 3 3 3

So the answer is n^2 + 3.