document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051855>Question 1051855</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a and b if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+ak%2Bb%2C+k=1%2C+n+%29+=+8n%5E2%2B11n ALIGN=MIDDLE  ALT=\"sum%28+ak%2Bb%2C+k=1%2C+n+%29+=+8n%5E2%2B11n\"   DISABLED_style= \"max-width:90%; height:auto;\" >, given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+k%2C+k=1%2C+n+%29+=+%28n%28n%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"sum%28+k%2C+k=1%2C+n+%29+=+%28n%28n%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667325 by </B><A HREF=/tutors/aboutme.mpl?userid=Bakr.R><B>Bakr.R(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Bakr.R><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=Bakr.R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Thank you Edwin, that was actually extremely helpful and a unique method, it wasn't how I would tackle the problem, but the question did ask a series of questions prior (in my maths textbook) to force me to use the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+k%2C+k=1%2C+n+%29+=+%28n%28n%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"sum%28+k%2C+k=1%2C+n+%29+=+%28n%28n%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the answer (with the word \"Hence\"), so although your method works efficiently (and far more easily), a specific method was requested, and for those seeking that particular method, (I found during this question was being solved) here's how it was done.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+ak%2Bb%2C+k=1%2C+n+%29+=+8n%5E2%2B11n ALIGN=MIDDLE  ALT=\"sum%28+ak%2Bb%2C+k=1%2C+n+%29+=+8n%5E2%2B11n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With added coefficients, we can separate the terms each with its own sum, we reach:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+ak%2C+k=1%2C+n+%29+%2Bsum%28+b%2C+k=1%2C+n+%29+ ALIGN=MIDDLE  ALT=\"sum%28+ak%2C+k=1%2C+n+%29+%2Bsum%28+b%2C+k=1%2C+n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we earlier found out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+k%2C+k=1%2C+n+%29+=+%28n%28n%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"sum%28+k%2C+k=1%2C+n+%29+=+%28n%28n%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We may deduce that (with substitution)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2An%28n%2B1%29%2F2%2Bsum%28+b%2C+k=1%2C+n+%29+ ALIGN=MIDDLE  ALT=\"a%2An%28n%2B1%29%2F2%2Bsum%28+b%2C+k=1%2C+n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and with coefficient b being the only term,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2An%28n%2B1%29%2F2%2Bbn+ ALIGN=MIDDLE  ALT=\"a%2An%28n%2B1%29%2F2%2Bbn+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since b is the only term and is a constant)<BR>\n" );
document.write( "We expand terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28an%5E2%2Ban%29%2F2%2Bbn+=+8n%5E2%2B11n ALIGN=MIDDLE  ALT=\"%28an%5E2%2Ban%29%2F2%2Bbn+=+8n%5E2%2B11n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We now follow a method of comparing coefficiants marked by the same variable, having each coefficient match its opposing equal value.<BR>\n" );
document.write( "By splitting fractions to factorize to one variable of each, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=an%5E2%2F2%2Ban%2F2%2Bbn+=+8n%5E2%2B11n ALIGN=MIDDLE  ALT=\"an%5E2%2F2%2Ban%2F2%2Bbn+=+8n%5E2%2B11n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=an%5E2%2F2%2Bn%28a%2F2%2Bb%29=+8n%5E2%2B11n ALIGN=MIDDLE  ALT=\"an%5E2%2F2%2Bn%28a%2F2%2Bb%29=+8n%5E2%2B11n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=an%5E2%2F2=8n%5E2 ALIGN=MIDDLE  ALT=\"an%5E2%2F2=8n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F2=8 ALIGN=MIDDLE  ALT=\"a%2F2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=16 ALIGN=MIDDLE  ALT=\"a=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And moving to the second comparison,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28a%2F2%2Bb%29=11n ALIGN=MIDDLE  ALT=\"n%28a%2F2%2Bb%29=11n\"   DISABLED_style= \"max-width:90%; height:auto;\" > We may substitute a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2816%2F2%2Bb%29=11n ALIGN=MIDDLE  ALT=\"n%2816%2F2%2Bb%29=11n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Bb=11 ALIGN=MIDDLE  ALT=\"8%2Bb=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And with that relation we find a=16, b=3 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );