Calculus Polynomial

Question

Suppose an = 3n^2+7n+8. Find a closed formula for the sequence of differences by computing an−an−1

Answer 1

Traditionally Δa_n is defined to be a_n+1 - a_n.

a_n= 3n² + 7n + 8

a_n-1 = 3(n-1)² + 7(n-1) +8

Now expand a_n-1, do the subtraction and collect terms and you will get the required answer.