Question

here are the first four tearms of a sequence 1, 11, 22, 37, find and express in terms of n the nth term of this sequence

Answer 1

2n² + n + 1

Explanation:

The sequence is 4, 11, 22, 37

Difference between:  7, 11, 15

The first differences are 7, 11, 15, and the second differences are 4.

Since half of 4 is 2, then the first term will be 2n^2.

Subtracting 2n² from the sequence gives 2, 3, 4, 5 which has nth term n + 1.

Therefore the final answer is 2n² + n + 1