Try this beautiful Problem based on Number Pattern from AMC 8 2020.
Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?
Number Pattern
Sequence
Visualization
AMC 8 2020 Problem 4
37
Try to see the three figures carefully
First hexagon has one dot and second hexagon has 7 dots. And the 3rd hexagon has dots.
Now, If we notice carefully , we have We have $h_{1}=1$ and $h_{n+1}=h_{n}+6 n$.where, $h_{n}$ denote the number of dots in the $n$th hexagon.
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