document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159183>Question 159183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My math teacher has asked me to find the n^th term for the fourth diagonal in Pascal's Triangle. Basicly, he has asked me to find a formula that will find the next number for the fourth diagonal. I've tried all sorts of charts to derieve a formula but none have yeilded any.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117306 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=117306\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation for the 3d diagonal is given as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B1%29%2An%29%2F2 ALIGN=MIDDLE  ALT=\"%28%28n%2B1%29%2An%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the equation for the 4th diagonal is given as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B2%29%2A%28n%2B1%29%2A%28n%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28%28n%2B2%29%2A%28n%2B1%29%2A%28n%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "try these websites.<BR>\n" );
document.write( "the first one describes pascal's triangle.<BR>\n" );
document.write( "the second one actually give you equations to calculat the nth term.<BR>\n" );
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document.write( "the first website is:       http://www.mathsisfun.com/tetrahedral-number.html<BR>\n" );
document.write( "the second website is:      http://noticingnumbers.net/220PASCALStriangle.htm<BR>\n" );
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document.write( "the formulas i provided you are taken from the second website and manipulated so the manual calculations are easier.<BR>\n" );
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document.write( "a test of the formulas for the 9th term is constructed below.<BR>\n" );
document.write( "the answer should be 45 for the 3d diagonal and 165 for the 4th diagonal.<BR>\n" );
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document.write( "for the 3d diagonal, the formula for the 9th term (n = 9) yields<BR>\n" );
document.write( "(10*9)/2 which equals 90/2 which equals 45 which is correct.<BR>\n" );
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document.write( "for the 4th diagonal, the formula for the 9th term (n = 9) yields<BR>\n" );
document.write( "(11*10*9)/6 = 990/6 = 165.<BR>\n" );
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document.write( "these formulas actually work !!!!!<BR>\n" );
document.write( "hopefully this is what you were looking for.\r<BR>\n" );
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