Answers created by Yosief

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• Show all Polygonal Sequences can be generated by solving the Matrix equation #Avec(x)= vec(b)# where #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#?