Question

look at this pattern:
(i cant type the pattern...)
figure one: 1 hexagon
figure 2: 3 hexagons
figure 3: 5 hexagons
figure 4: 10 hexagons

if this pattern continues, figure 20 will have 210 hexagons. how many hexagons will figure 21 have?

Answer 1

Are the hexagons touching each other?

Answer 2

yes

Answer 3

ok so the 2nd figure would be: ?

Answer 4

heres a pic

Answer 5

OHHH ok. So figure one has one hexagon. Figure two has two hexagons stacked to the left and up of the single one. Then figure 3 has 3 hexagons stacked to the left and up of those two. So a pattern you could find is that the figure number corresponds to the number of hexagons on one side of the triangle formed by the hexagons...I know that's a bit confusing but does that make sense?

Answer 6

So this is really having to do with a factorial relationship (just adding, not multiplying).
Figure one: 1
Figure two: 1+2
figure three1+2+3
...
figure twenty: 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20 hexagons

Answer 7

so it would be 220, i think right?

Answer 8

if figure twenty has 210, then figure twenty one has 210+21 so fig 21 has 231 hexagons.

Answer 9

ok thank you! :)

Answer 10

Sure :)