Question 1064253: A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure we have 3 rows of small congruent equilateral triangles, with 5 small triangles in the base row. How many toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of 2003 small equilateral triangles?
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure we have 3 rows of small congruent equilateral triangles, with 5 small triangles in the base row.
top row has 3 picks
2nd row has 3+3 = 6 picks
base row has 3+3+3 = 9 picks
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Arithmetic Sequence with a(1) = 3 , d = 3 and n = 3
# of picks = (3/2)(3+9) = 3*6 = 18
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How many toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of 2003 small equilateral triangles?
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1st row:: 1 triangle
2nd row:: 3 triangles
3rd row:: 5 triangles
nth row:: 2003 triangles
Row Arithmetic Sequence with a(1) = 1, d = 2, a(n) = 2003
1 + (n-1)2 = 2003
2n-1 = 2003
n = 1002 rows
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Toothpick Arithmetic Sequence
1st row:: 3
2nd row:: 6
3rd row:: 9
1003 row:: 3009
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Ans: S(1002) = (1002/2)(3+3009) = 501(3012) = 1509012 tootpicks
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Cheers,
Stan H.
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