Using finite differences or an approach of your choosing, find the general term for the following polygonal numbers. Show your work

a. The general term for the t_n stage for the dodecagon (12 sided polygon). The values for the first 5 stages are 1, 12, 33, 64, 105

b. Find the general term for the tn stage and the general number term for the k-sided polygon (s_k). If the generalization for the columns and rows is not the same, show your generalization for the tn stage and the s_k polygon are equivalent. A table is shown.

Table for Polygonal Numbers Polygonal Number ti t2 t3 t4 ts tn 1 3 6 10 15 Triangular S= 3 1 4 9 16 25 Square S=4 1 5 12 22 35 Pentagonal S=5 1 6 15 28 45 Hexagonal S= 6 1 7 18 34 55 Heptagonal S= 7 1 8 21 40 65 Octagonal S= 8 1 12 Dodecagon S= 12 S agonal S=k Table for Polygonal Numbers Polygonal Number ti t2 t3 t4 ts tn 1 3 6 10 15 Triangular S= 3 1 4 9 16 25 Square S=4 1 5 12 22 35 Pentagonal S=5 1 6 15 28 45 Hexagonal S= 6 1 7 18 34 55 Heptagonal S= 7 1 8 21 40 65 Octagonal S= 8 1 12 Dodecagon S= 12 S agonal S=k