document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209569>Question 1209569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1 + 4 + 7 + 10 + ... + x = 287<BR>\n" );
document.write( "find x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849547 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13216)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "For an arithmetic sequence....<br><BR>\n" );
document.write( "Sum = (number of terms)*(average of terms)<br><BR>\n" );
document.write( "Number of terms: ((last term minus first term)/common difference)+1<br><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F3%2B1=%28x%2B2%29%2F3 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F3%2B1=%28x%2B2%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Average of terms = average of first and last terms = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The sum is 287:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B2%29%2F3%29%28%28x%2B1%29%2F2%29=287 ALIGN=MIDDLE  ALT=\"%28%28x%2B2%29%2F3%29%28%28x%2B1%29%2F2%29=287\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B3x%2B2%29%2F6=287 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B3x%2B2%29%2F6=287\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x%2B2=1722 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x%2B2=1722\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-1720=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-1720=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B43%29%28x-40%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B43%29%28x-40%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "-----------------------------------------------------------------------<br><BR>\n" );
document.write( "A hint for doing that factoring.... We want to write<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-1720=%28x%2Ba%29%28x-b%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-1720=%28x%2Ba%29%28x-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since the linear coefficient is 3, a and b are \"close together\".  So let them be \"approximately equal\".  Then 1720 is \"close to\" a perfect square. The square root of 1720 is a bit more than 40; and since the product ab has final digit 0, one of a or b should be 40.  Then a bit of arithmetic shows that a and b are in fact 43 and 40.<br><BR>\n" );
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document.write( "Obviously ignore the negative solution....<br><BR>\n" );
document.write( "ANSWER: x=40<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );