-5 -4 -1 4 11 20 31 Nth term

Question

-5 -4 -1 4 11 20 31

Answer 1

The differences between each pair have the sequence 1, 3, 5, 7,...

The sum of these are the squares of the natural numbers: 1, 4, 9, 16,...

Take the first few of numbers in the series: -5, -4, -1, 4.

-5+0=-5; -5+1=-4, -5+4=-1, -5+9=4.

So the nth term is -5+(n-1)². We could use this formula.

We can expand this. -5+n²-2n+1=n²-2n-4, so we could use this equivalent formula. Example: put n=7, then we have -5+36=31, or 49-14-4=31 as the 7th term.

Answer 2

What is the Nth term for −5,−4,−1,4,11,20,31