Question

Answer A this first graphwhat is the relationship please fill in the graph and what is the explicit function help

Answer 1

To find the nth term of a sequence in which the difference between term is changing we can use the formula

$a_n=a+(n-1)d+\frac{1}{2}(n-1)(n-2)c$

where a is the first term, d is the difference between the first two terms and c is the differences between the differences.

In A, we see that a=11, d=3 and c=2. Then

$\begin{gathered} a_n=11+3(n-1)+\frac{1}{2}\cdot2(n-1)(n-2) \\ =11+3n-3+n^2-3n+2 \\ =n^2+10 \end{gathered}$

Therefore the nth term for the first table is

$a_n=n^2+10$