document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725436>Question 725436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "I know how to find the sum of n consecutive integers. <BR>\n" );
document.write( "I use the formula: n(n+1)/2\r<BR>\n" );
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document.write( "But my problem is: The sum of n consecutive integers is 120. Find n.\r<BR>\n" );
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document.write( "My approach is nsq+n = 240<BR>\n" );
document.write( "Now what is the easy way to find n?\r<BR>\n" );
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document.write( "I can do this by going from the answer to the question and guessing the number. But is there a easy way to find what n is.\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Jay </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444175 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=444175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you have studied polynomials and/or quadratic equations,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn=240 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn=240\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn-240=0 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn-240=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At that point you would solve either<BR>\n" );
document.write( "by factoring,<BR>\n" );
document.write( "or by \"completing the square\",<BR>\n" );
document.write( "or by using the quadratic formula.<BR>\n" );
document.write( " <BR>\n" );
document.write( "However, it is easier to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29=240 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by finding two consecutive numbers whose product is 240.<BR>\n" );
document.write( " <BR>\n" );
document.write( "You could find factors from 1 up, and they would come in pairs:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=1%2A240 ALIGN=MIDDLE  ALT=\"240=1%2A240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=2%2A120 ALIGN=MIDDLE  ALT=\"240=2%2A120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=3%2A80 ALIGN=MIDDLE  ALT=\"240=3%2A80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=4%2A60 ALIGN=MIDDLE  ALT=\"240=4%2A60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=5%2A48 ALIGN=MIDDLE  ALT=\"240=5%2A48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=6%2A40 ALIGN=MIDDLE  ALT=\"240=6%2A40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7 is not a factor<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=8%2A30 ALIGN=MIDDLE  ALT=\"240=8%2A30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "9 is not a factor<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=10%2A24 ALIGN=MIDDLE  ALT=\"240=10%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and so on.<BR>\n" );
document.write( " <BR>\n" );
document.write( "But if you have some factoring practice, the answer will jump at you.<BR>\n" );
document.write( "It is obvious that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=8%2A30%7D%7D%2C+right%3F%0D%0A%7B%7B%7B240=8%2A30 ALIGN=MIDDLE  ALT=\"240=8%2A30%7D%7D%2C+right%3F%0D%0A%7B%7B%7B240=8%2A30\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2A2%29%2A%2830%2F2%29=16%2A15 ALIGN=MIDDLE  ALT=\"%288%2A2%29%2A%2830%2F2%29=16%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the product of two consecutive numbers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=15%29 ALIGN=MIDDLE  ALT=\"highlight%28n=15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n%2B1=16%29 ALIGN=MIDDLE  ALT=\"highlight%28n%2B1=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=16%2A15 ALIGN=MIDDLE  ALT=\"240=16%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" > is what you would need to figure out to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn-240=0 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn-240=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > by factoring, anyway. </SPAN>\n" );
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