document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064253>Question 1064253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679304 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=679304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
document.write( "top row has 3 picks<BR>\n" );
document.write( "2nd row has 3+3 = 6 picks<BR>\n" );
document.write( "base row has 3+3+3 = 9 picks<BR>\n" );
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document.write( "Arithmetic Sequence with a(1) = 3 , d = 3 and n = 3<BR>\n" );
document.write( "# of picks = (3/2)(3+9) = 3*6 = 18<BR>\n" );
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document.write( " 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?<BR>\n" );
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document.write( "1st row:: 1 triangle<BR>\n" );
document.write( "2nd row:: 3 triangles<BR>\n" );
document.write( "3rd row:: 5 triangles<BR>\n" );
document.write( "nth row:: 2003 triangles<BR>\n" );
document.write( "Row Arithmetic Sequence with a(1) = 1, d = 2, a(n) = 2003<BR>\n" );
document.write( "1 + (n-1)2 = 2003<BR>\n" );
document.write( "2n-1 = 2003<BR>\n" );
document.write( "n = 1002 rows<BR>\n" );
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document.write( "Toothpick Arithmetic Sequence <BR>\n" );
document.write( "1st row:: 3<BR>\n" );
document.write( "2nd row:: 6<BR>\n" );
document.write( "3rd row:: 9<BR>\n" );
document.write( "1003 row:: 3009<BR>\n" );
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document.write( "Ans: S(1002) = (1002/2)(3+3009) = 501(3012) = 1509012 tootpicks<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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