. Suppose you have a sequence that begins {0, 2, 6, 12}.Give the next 3 numbers in your sequence. Use a positional definition to define your sequence.

Question

Can I have a breakdown to better understand. I am wanting to double check my work to make sure I am on the right track of solving these kind of problems.

Answer 1

The first differences of the sequence are 2, 4, 6.

Presumably the next differences are 8, 10, 12 and the numbers in sequence are 20, 30, and 42; this sequence is 

n² + n for integer n greater than or equal to 0.

 

When the first differences in a sequence are an arithmetic progression, the sequence is always a 2nd degree polynomial and it is pretty easy to prove that.  For an old but thorough reference try to find "Calculus of Finite Differences" by Jordan.