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The first three stages of a pattern are shown below, in which each line segment represents a toothpick. If the pattern continues such that at each successive stage, three toothpicks are added to the previous arrangement, how many toothpicks are necessary to create the arrangement for the 250th stage?

 

Thank you in advance

-wolf

 Sep 22, 2019

4+0 Answers

 #1
avatar+36916 
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No diagram?

If each stage takes 3 toothpicks,  250 x 3 = 750

 Sep 22, 2019
 #2
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I AM SOO SRRy, I forgot the digram, here it is,

 Sep 22, 2019
 #3
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The "generating function" appears to be:
a(n) =n * 3 + 1. So:
First term =1 * 3 + 1 = 4
2nd term   =2 * 3 + 1 = 7
3rd term    =3 * 3 + 1 = 10......and so on. 
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250th term =250 * 3 + 1 = 751 toothpicks.

 Sep 22, 2019
 #4
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THANK YOU - wolf

Guest Sep 22, 2019

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