How do I get the equation for the 10th, 20th and nth members in the sequence?
The sequence is,
1. 1x1; 1 square; 4 matchsticks
2. 2x2; 2 squares; 12 matchsticks
3. 3x3; 9 squares; 24 matchsticks
How do I find the pattern to make the equation to find the 10th, 20th, and nth members of the sequence?
1 Answer | Add Yours
Each horizontal lines will have 10 matchsticks.
You will have 11 horizontal lines
Therefore you will have 10*11 horizontal matchsticks
Same work with the vertical matchsticks
You will have 11 vertical lines of 10 matchsticks.
therefore you will have 11*10=110 vertical matchsticks.
In total you will have 220=2*11*10
If you have a 20x20 square.
Again you will have 21 horizontal lines of 20 matchsticks and 21 vertical lines of 20 matchsticks. Therefore you have 20*21*2 matchsticks in total.
Now for a nxn square
we have horizontal n+1 horizontal lines of n matchsticks and n+1 vertical lines of n matchsticks. In total we have n*(n+1)*2 matchsticks.
Therefore the formula is 2n(n+1) matchsticks for a n x n square.
It is matches the result for n=10, n=20 and of course n=1 n=2, n=3.
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