1- On the first ring you have 1 hexagon,
on the second you have 6, on the third : 12, and on the 4th : 18
The total number of hexagons is 1+6+12+18=37
f(4)=3*4^2-3*4+1=3*16-12+1=37. The polynomial function f(r) gives the total number of hexagons when r=4
2- We have from the second ring an arithmetic suite u1=6 , u2=12, u3=18,
u4 should be 24 and so on. We are going to calculate the sum from u1 until u19 (20 rings including u0=1)
let's calculate u19=6+(19-1)*6=144
S=u1+...+u19=(u1+u19)*19/2=1140 and we have to add 1 hexagon for the 1st ring so the final result is 1141 hexagons.
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