document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055828>Question 1055828</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that four integers are consecutive terms of an arithmetic sequence with sum 24 and product 945, what is the biggest of these four integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670977 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=670977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since it is about 4 integers, consider divisibility.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=945=3%5E3%2A5%2A7 ALIGN=MIDDLE  ALT=\"945=3%5E3%2A5%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the factorization for 945.<BR>\n" );
document.write( "You notice that 3, 5, and 7 are factors of 945,<BR>\n" );
document.write( "and the form an arithmetic sequence!<BR>\n" );
document.write( "If those were 3 of the 4 factors whose product is 954,<BR>\n" );
document.write( "The fourth factor would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=945%2F%283%2A5%2A7%29=3%5E3%2A5%2A7%2F%283%2A5%2A7%29=3%5E3=9 ALIGN=MIDDLE  ALT=\"945%2F%283%2A5%2A7%29=3%5E3%2A5%2A7%2F%283%2A5%2A7%29=3%5E3=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A5%2A7%2A9=945 ALIGN=MIDDLE  ALT=\"3%2A5%2A7%2A9=945\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and those 4 factors form an arithmetic sequence.<BR>\n" );
document.write( "Of course, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > are another answer.<BR>\n" );
document.write( " <BR>\n" );
document.write( "USING EQUATIONS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= common difference of the arithmetic sequence.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F4=6 ALIGN=MIDDLE  ALT=\"24%2F4=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >= average (mean) and median of thev4 numbers.<BR>\n" );
document.write( "Then, the numbers are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-3x ALIGN=MIDDLE  ALT=\"6-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-x ALIGN=MIDDLE  ALT=\"6-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bx ALIGN=MIDDLE  ALT=\"6%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B3x ALIGN=MIDDLE  ALT=\"6%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The product is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-3x%29%286-x%29%286%2Bx%29%286%2B3x%29=945 ALIGN=MIDDLE  ALT=\"%286-3x%29%286-x%29%286%2Bx%29%286%2B3x%29=945\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%5E2-%283x%29%5E2%29%286%5E2-x%5E2%29=945 ALIGN=MIDDLE  ALT=\"%286%5E2-%283x%29%5E2%29%286%5E2-x%5E2%29=945\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836-9x%5E3%29%2836-x%5E2%29=945 ALIGN=MIDDLE  ALT=\"%2836-9x%5E3%29%2836-x%5E2%29=945\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%284-x%5E3%29%2836-x%5E3%29=945 ALIGN=MIDDLE  ALT=\"9%284-x%5E3%29%2836-x%5E3%29=945\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-x%5E3%29%2836-x%5E2%29=105 ALIGN=MIDDLE  ALT=\"%284-x%5E3%29%2836-x%5E2%29=105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144-40x%5E2%D7x%5E4=105 ALIGN=MIDDLE  ALT=\"144-40x%5E2%D7x%5E4=105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-40x%2B39=0 ALIGN=MIDDLE  ALT=\"x%5E4-40x%2B39=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-1%29%28x%5E3-39%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-1%29%28x%5E3-39%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "EITHER,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=1%2C%22or%22%2Cx=-1%29 ALIGN=MIDDLE  ALT=\"system%28x=1%2C%22or%22%2Cx=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which gives you the two arithmetic sequences found before,<BR>\n" );
document.write( "OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=39 ALIGN=MIDDLE  ALT=\"x%5E2=39\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which gives you<BR>\n" );
document.write( "two arithmetic sequences of four (irrational) numbers,<BR>\n" );
document.write( "asking up to 24, and with a product of 945. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );