Question

What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79 Please could someone help me and write a step by step explanation? Thanks :D

Answer 1

Explanation:

The first differences are 7,9,11,13,15,17 and the second differences are 2.

This means that the first term of the sequence is n^2.

Subtracting n^2 from the sequence gives 6,10,14,18,22,26, which has nth term of 4n + 2.

So putting these together gives a nth term of the quadratic sequence of n^2 + 4n + 2.

Hope it helped and tell me if I went wrong :)