calculus polynomial

Question

Suppose an = 2n2−2n+7. Find a closed formula for the sequence of differences by computing an−an−1.

Answer 1

an = 2n^2 -2n +7

an-1 = 2(n-1)^2 -2(n-1)+ 7 = 2(n^2-2n+1) -2n+2 +7 = 2n^2 -4n+2 -2n+7

= 2n^2 -6n + 9

an - an-1 = 2n^2 -2n+7 - 2n^2 +6n-9 = 4n-2

an -an-1 = 4n-2