Answers created by Yosief

Back to user's profile
Show all Polygonal Sequences can be generated by solving the Matrix equation $A \to x = \to b$ $Avec(x)= vec(b)$ where $A$ $A$ is $[[1, 1, 1], [4, 2, 1], [9,3,1]]$ and $vec(b)=[[a_1], [a_2], [a_3]]$ is the column vector? Show that $vec(x) =A^-1vec(b)$ for all sequences?
Show that all Polygonal sequences generated by the Series of Arithmetic sequence with common difference $d, d in ZZ$ are polygonal sequences that can be generated by $a_n = an^2+bn+c$ ?
Let $a_n$ be a sequence given by: ${1, 6, 15, 28, 45,66,..., f(n)}$ . Show that the generating function $f(n)$ is of the form $an^2 + bn + c$ . Find the formula by computing the coefficients $a, b, c$ ?
Let $S_n$ be a polygonal sequence built by the Series of the Arithmetic Sequence $S_n = Sigma_i^(n)a_i$ where $a_n = {1, 4, 7, 10, 13, ...}$ , find the generating formula for polygonal sequence $S_n$ ?