AMC 8 2020 Problem 4 | Dot Pattern Problem

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?

• 35
• 37
• 39
• 43
• 49

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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