document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178152>Question 1178152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider each given sequence start.  i) Classify each as arithmetic, geometric, and/or none of these.  ii)  Find the 28th term.  iii)  Find the sum of the first 7 terms, call it S7 . <BR>\n" );
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document.write( "a)	44, −6, 44, −4,  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807325 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,...\r<BR>\n" );
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document.write( "1st term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=44 ALIGN=MIDDLE  ALT=\"a%5B1%5D=44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2nd term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=-6=44-50 ALIGN=MIDDLE  ALT=\"a%5B2%5D=-6=44-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3rd term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=-4=44-48 ALIGN=MIDDLE  ALT=\"a%5B3%5D=-4=44-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> no common difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-4%2F44=-1%2F11 ALIGN=MIDDLE  ALT=\"r=-4%2F44=-1%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=44%2F-6=-22%2F3 ALIGN=MIDDLE  ALT=\"r=44%2F-6=-22%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> no common ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "i) Classify each as arithmetic, geometric, and/or none of these. \r<BR>\n" );
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document.write( "=> no common difference <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, no common ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the sequence is neither arithmetic nor geometric\r<BR>\n" );
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document.write( "to find  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term formula use differences:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................\r<BR>\n" );
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document.write( ".............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................\r<BR>\n" );
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document.write( "....................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >rd difference, so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term formula<BR>\n" );
document.write( " will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >rd degree function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=an%5E3%2Bbn%5E2%2Bcn%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%5D=an%5E3%2Bbn%5E2%2Bcn%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " plug in some of the values from the sequence, and then solving the resulting system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=an%5E3%2Bbn%5E2%2Bcn%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%5D=an%5E3%2Bbn%5E2%2Bcn%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >->first term, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=a%2A1%5E3%2Bb%2A1%5E2%2Bc%2A1%2Bd ALIGN=MIDDLE  ALT=\"44=a%2A1%5E3%2Bb%2A1%5E2%2Bc%2A1%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=a%2Bb%2Bc%2Bd ALIGN=MIDDLE  ALT=\"44=a%2Bb%2Bc%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=an%5E3%2Bbn%5E2%2Bcn%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%5D=an%5E3%2Bbn%5E2%2Bcn%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >->first term, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2 ALIGN=MIDDLE  ALT=\"n=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6=a%2A2%5E3%2Bb%2A2%5E2%2Bc%2A2%2Bd ALIGN=MIDDLE  ALT=\"-6=a%2A2%5E3%2Bb%2A2%5E2%2Bc%2A2%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6=8a%2B4b%2B2c%2Bd ALIGN=MIDDLE  ALT=\"-6=8a%2B4b%2B2c%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >............eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=a%2A3%5E3%2Bb%2A3%5E2%2Bc%2A3%2Bd ALIGN=MIDDLE  ALT=\"44=a%2A3%5E3%2Bb%2A3%5E2%2Bc%2A3%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=27a%2B9b%2B3c%2Bd ALIGN=MIDDLE  ALT=\"44=27a%2B9b%2B3c%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=a%2A4%5E3%2Bb%2A4%5E2%2Bc%2A4%2Bd ALIGN=MIDDLE  ALT=\"-4=a%2A4%5E3%2Bb%2A4%5E2%2Bc%2A4%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=64a%2B16b%2B4c%2Bd ALIGN=MIDDLE  ALT=\"-4=64a%2B16b%2B4c%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >............eq.4\r<BR>\n" );
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document.write( "subtract eq.1 from eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6-44=+8a%2B4b%2B2c%2Bd+-%28a%2Bb%2Bc%2Bd%29 ALIGN=MIDDLE  ALT=\"-6-44=+8a%2B4b%2B2c%2Bd+-%28a%2Bb%2Bc%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50=+8a%2B4b%2B2c%2Bd+-a-b-c-d%29 ALIGN=MIDDLE  ALT=\"-50=+8a%2B4b%2B2c%2Bd+-a-b-c-d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50=+7a%2B3b%2Bc ALIGN=MIDDLE  ALT=\"-50=+7a%2B3b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............eq.3\r<BR>\n" );
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document.write( "subtract eq.1 from eq.3 (reason: next term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" > again)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44-44=+27a%2B9b%2B3c%2Bd-%28a%2Bb%2Bc%2Bd%29 ALIGN=MIDDLE  ALT=\"44-44=+27a%2B9b%2B3c%2Bd-%28a%2Bb%2Bc%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+27a%2B9b%2B3c%2Bd-a-b-c-d ALIGN=MIDDLE  ALT=\"0=+27a%2B9b%2B3c%2Bd-a-b-c-d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+26a%2B8b%2B2c ALIGN=MIDDLE  ALT=\"0=+26a%2B8b%2B2c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26a-2c=8b ALIGN=MIDDLE  ALT=\"-26a-2c=8b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-26a%2F8-2c%2F8 ALIGN=MIDDLE  ALT=\"b=-26a%2F8-2c%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-13a%2F4-c%2F4 ALIGN=MIDDLE  ALT=\"b=-13a%2F4-c%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............eq.4\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50=+7a%2B3%28-13a%2F4-c%2F4%29%2Bc ALIGN=MIDDLE  ALT=\"-50=+7a%2B3%28-13a%2F4-c%2F4%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.3...., substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50=+c%2F4+-+%2811a%29%2F4 ALIGN=MIDDLE  ALT=\"-50=+c%2F4+-+%2811a%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50%2B%2811a%29%2F4=c%2F4 ALIGN=MIDDLE  ALT=\"-50%2B%2811a%29%2F4=c%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200%2B11a=c ALIGN=MIDDLE  ALT=\"-200%2B11a=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......................eq.5\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-13a%2F4-c%2F4 ALIGN=MIDDLE  ALT=\"b=-13a%2F4-c%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............eq.4, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-13a%2F4-%28-200%2B11a%29%2F4 ALIGN=MIDDLE  ALT=\"b=-13a%2F4-%28-200%2B11a%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=50+-+6a ALIGN=MIDDLE  ALT=\"b=50+-+6a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.................eq.6\r<BR>\n" );
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document.write( "subtract eq.1 from eq.4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-44=64a%2B16b%2B4c%2Bd-%28a%2Bb%2Bc%2Bd%29 ALIGN=MIDDLE  ALT=\"-4-44=64a%2B16b%2B4c%2Bd-%28a%2Bb%2Bc%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >............substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > from eq.6 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > from eq.5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-44=64a%2B16b%2B4c%2Bd-a-b-c-d ALIGN=MIDDLE  ALT=\"-4-44=64a%2B16b%2B4c%2Bd-a-b-c-d\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48=63a%2B15b%2B3c+ ALIGN=MIDDLE  ALT=\"-48=63a%2B15b%2B3c+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48=63a%2B15%2850+-+6a%29%2B3%28-200%2B11a%29+ ALIGN=MIDDLE  ALT=\"-48=63a%2B15%2850+-+6a%29%2B3%28-200%2B11a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48=63a%2B750+-+90a-600%2B33a+ ALIGN=MIDDLE  ALT=\"-48=63a%2B750+-+90a-600%2B33a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48=6a%2B150 ALIGN=MIDDLE  ALT=\"-48=6a%2B150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6a=-48-150 ALIGN=MIDDLE  ALT=\"6a=-48-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6a=-198 ALIGN=MIDDLE  ALT=\"6a=-198\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-33 ALIGN=MIDDLE  ALT=\"a=-33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
document.write( "go to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=50+-+6a ALIGN=MIDDLE  ALT=\"b=50+-+6a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.................substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=50+-+6%28-33%29 ALIGN=MIDDLE  ALT=\"b=50+-+6%28-33%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=50+%2B+198 ALIGN=MIDDLE  ALT=\"b=50+%2B+198\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=248 ALIGN=MIDDLE  ALT=\"b=248\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go to\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200%2B11a=c ALIGN=MIDDLE  ALT=\"-200%2B11a=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........................substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200%2B11%28-33%29=c ALIGN=MIDDLE  ALT=\"-200%2B11%28-33%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-200-363=c ALIGN=MIDDLE  ALT=\"-200-363=c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-563 ALIGN=MIDDLE  ALT=\"c=-563\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "go to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=a%2Bb%2Bc%2Bd ALIGN=MIDDLE  ALT=\"44=a%2Bb%2Bc%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=-33%2B248-563%2Bd ALIGN=MIDDLE  ALT=\"44=-33%2B248-563%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=-348%2Bd ALIGN=MIDDLE  ALT=\"44=-348%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44%2B348=d ALIGN=MIDDLE  ALT=\"44%2B348=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=392 ALIGN=MIDDLE  ALT=\"d=392\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, coefficients are:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-33 ALIGN=MIDDLE  ALT=\"a+=+-33\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+248 ALIGN=MIDDLE  ALT=\"b+=+248\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-563 ALIGN=MIDDLE  ALT=\"c+=+-563\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+392 ALIGN=MIDDLE  ALT=\"d+=+392\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and equation is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=-33n%5E3%2B248n%5E2-563n%2B392 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=-33n%5E3%2B248n%5E2-563n%2B392\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ii)  Find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B28%5D=-33%2A28%5E3%2B248%2A28%5E2-563%2A28%2B392 ALIGN=MIDDLE  ALT=\"a%5B28%5D=-33%2A28%5E3%2B248%2A28%5E2-563%2A28%2B392\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B28%5D=-545356 ALIGN=MIDDLE  ALT=\"a%5B28%5D=-545356\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "iii)  Find the sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+ ALIGN=MIDDLE  ALT=\"7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >terms, call it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S7 ALIGN=MIDDLE  ALT=\"S7\"   DISABLED_style= \"max-width:90%; height:auto;\" > . <BR>\n" );
document.write( "we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,...\r<BR>\n" );
document.write( "\n" );
document.write( "first find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >th, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >th, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=-33%2A5%5E3%2B248%2A5%5E2-563%2A5%2B392=-348 ALIGN=MIDDLE  ALT=\"a%5B5%5D=-33%2A5%5E3%2B248%2A5%5E2-563%2A5%2B392=-348\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=-33%2A6%5E3%2B248%2A6%5E2-563%2A6%2B392=-1186 ALIGN=MIDDLE  ALT=\"a%5B6%5D=-33%2A6%5E3%2B248%2A6%5E2-563%2A6%2B392=-1186\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B7%5D=-33%2A7%5E3%2B248%2A7%5E2-563%2A7%2B392=-2716 ALIGN=MIDDLE  ALT=\"a%5B7%5D=-33%2A7%5E3%2B248%2A7%5E2-563%2A7%2B392=-2716\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44 ALIGN=MIDDLE  ALT=\"44\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-348 ALIGN=MIDDLE  ALT=\"-348\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2716 ALIGN=MIDDLE  ALT=\"-2716\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2716 ALIGN=MIDDLE  ALT=\"-2716\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B7%5D=44-6%2B44-4-348-2716-2716+=-5702 ALIGN=MIDDLE  ALT=\"S%5B7%5D=44-6%2B44-4-348-2716-2716+=-5702\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );