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February 11th, 2019, 03:40 PM   #1
NMc
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Post Help!!

Ok, so I've been working on this question for days and nothing has been working.

The requirements are a rule (algebraic formula) for the matchstick pattern (e.g. x= n(n-1) 4n etc.)

Here is the table - PM me for the visual representation.

Item (x)= 1, 2, 3, 4,

Matchsticks (n)= 4, 12, 24, 40,

any help would be much appreciated.

(Just to clarify, 1 item = 4 matchsticks.)
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Last edited by skipjack; February 12th, 2019 at 06:04 PM.
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February 11th, 2019, 04:46 PM   #2
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1 ... 2x2

2 ... 3X4

3 ... 4x6

4 ... 5x8

see a pattern?
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February 12th, 2019, 12:59 AM   #3
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Hint: evaluate $\displaystyle \frac{\sqrt{2n + 1}}{2}$ for $n\,=$ 4, 12, 24, 40, etc.
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February 12th, 2019, 05:49 AM   #4
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Compare to triangulars:

1,3,6,10, .....

4,12,24,40, .....
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February 12th, 2019, 06:12 AM   #5
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The sequence (n)= 4,12,24,40... etc , is 2n(n+1) .
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February 12th, 2019, 07:17 AM   #6
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Quote:
Originally Posted by idontknow View Post
The sequence (n)= 4,12,24,40... etc , is 2n(n+1) .
....or TWICE the triangular number formula....
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February 12th, 2019, 09:11 AM   #7
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Except when it's four times.
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