Question

Fill in the blank for the explicit rule that produces this series.


-6, -3, 2, 9, 18, ...


a[n] = n^2 – _____

Answer 1

since the second common differences are a constant
then your sequence should be in the form
a[n]=An^2+Bn+C
it looks like they already give you A=1
so
a[n]=n^2+Bn+C
we can find B and C be using the numbers given in your sequence
use (1,-6) and (2,-3) two give you two equations
these 2 equations will allow you to solve for B and C

Answer 2

Thank you (:

Answer 3

np

Answer 4

\(\large\tt \begin{align} \color{black}{-6, -3, 2, 9, 18, ........\\~\\
1-7, 4-7-, 9-7, 16-7, 25-7, ........\\~\\
1^2-7, 2^2-7-, 3^2-7, 4^2-7, 5^2-7, ........\\~\\
}\end{align}\)