document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982206>Question 982206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Arithmetic Sequence Problem:<BR>\n" );
document.write( "A mosaic in the shape of an equilateral triangle is 25 ft on each side. Each tile in the mosaic is in the shape of an equilateral triangle, 12 inches to a side. The tiles are alternate in colour like &#9651;&#9662;&#9651; (sorry I cant show the picture) . How many tiles of each colour will be needed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603094 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each tile in the mosaic is in the shape of an equilateral triangle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12inches=1foot ALIGN=MIDDLE  ALT=\"12inches=1foot\"   DISABLED_style= \"max-width:90%; height:auto;\" > to a side.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "On the base of that triangular mosaic,<BR>\n" );
document.write( "you have the bases of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > tiles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Tiles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be at all 3 vertices of the triangular mosaic,<BR>\n" );
document.write( "and all 3 sides of the triangular mosaic would look just the same,<BR>\n" );
document.write( "so it does not matter which one I choose to call the base of the triangular mosaic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In between the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > base-down, vertex-up triangles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "there will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-1=24 ALIGN=MIDDLE  ALT=\"25-1=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > base-up, vertex-down triangles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "completing the first row/layer of tiles at the base of the triangular mosaic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Atop each of those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > base-up, vertex-down triangles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "there will be one base-down, vertex-up triangle of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "for a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > base-down, vertex-up triangles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "on the second row of the triangular mosaic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In between the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > base-down, vertex-up triangles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the second row,<BR>\n" );
document.write( "there will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24-1=23 ALIGN=MIDDLE  ALT=\"24-1=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > base-up, vertex-down triangles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "completing the second row/layer of tiles at the base of the triangular mosaic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That patter repeats, so you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5BX%5D=25%2B24%2B23%2B%22...%22%2B3%2B2%2B1 ALIGN=MIDDLE  ALT=\"N%5BX%5D=25%2B24%2B23%2B%22...%22%2B3%2B2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > tiles of color <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5BY%5D=24%2B23%2B22%2B%22...%22%2B3%2B2%2B1%7D%7D+tiles+of+color+%7B%7B%7BY ALIGN=MIDDLE  ALT=\"N%5BY%5D=24%2B23%2B22%2B%22...%22%2B3%2B2%2B1%7D%7D+tiles+of+color+%7B%7B%7BY\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Those numbers are the sums of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > first terms of the arithmetic sequence with first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and common difference <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The easiest way to calculate the sum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2B%22...%22%2Ba%5Bn-2%5D%2Ba%5Bn-1%5D%2Ba%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2B%22...%22%2Ba%5Bn-2%5D%2Ba%5Bn-1%5D%2Ba%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > when you know<BR>\n" );
document.write( "the number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > of terms you are adding,<BR>\n" );
document.write( "the first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > you are adding, and<BR>\n" );
document.write( "the last term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > you are adding is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2B%22...%22%2Ba%5Bn-2%5D%2Ba%5Bn-1%5D%2Ba%5Bn%5D=n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5BY%5D=24%2A%2824%2B1%29%2F2=12%2A25=highlight%28300%29 ALIGN=MIDDLE  ALT=\"N%5BY%5D=24%2A%2824%2B1%29%2F2=12%2A25=highlight%28300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5Bx%5D=N%5BY%5D%2B25=300%2B25=highlight%28325%29 ALIGN=MIDDLE  ALT=\"N%5Bx%5D=N%5BY%5D%2B25=300%2B25=highlight%28325%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );