document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855486>Question 855486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sixth term of an AP is 37 and the tenth term 53.Find the first term. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515387 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=515387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> MENTAL MATH (for multiple choice tests):<BR>\n" );
document.write( "from one number to the next you are adding a common difference.<BR>\n" );
document.write( "From the sixth term to the tenth term that common difference was added 4 times because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-6=4 ALIGN=MIDDLE  ALT=\"10-6=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means that the common difference is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2853-37%29%2F4=16%2F4=4 ALIGN=MIDDLE  ALT=\"%2853-37%29%2F4=16%2F4=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "From the first term to the sixth term that common difference was added 5 times because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-1=5 ALIGN=MIDDLE  ALT=\"6-1=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means that the common difference (4) was added 5 times, so the first term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37-5%2A4=37-20=highlight%2817%29 ALIGN=MIDDLE  ALT=\"37-5%2A4=37-20=highlight%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is a lot of words, but you can think through the concepts and calculations much faster than you can explain and write them.<BR>\n" );
document.write( " <BR>\n" );
document.write( "USING FORMULAS (to please the teacher by \"showing your work\"):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= first term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= common difference<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" >= general formula for term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=6 ALIGN=MIDDLE  ALT=\"n=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > we know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=a%5B1%5D%2B%286-1%29%2Ad=a%5B1%5D%2B5%2Ad=37 ALIGN=MIDDLE  ALT=\"a%5B6%5D=a%5B1%5D%2B%286-1%29%2Ad=a%5B1%5D%2B5%2Ad=37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10 ALIGN=MIDDLE  ALT=\"n=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > we know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B10%5D=a%5B1%5D%2B%2810-1%29%2Ad=a%5B1%5D%2B9%2Ad=53 ALIGN=MIDDLE  ALT=\"a%5B10%5D=a%5B1%5D%2B%2810-1%29%2Ad=a%5B1%5D%2B9%2Ad=53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%5B1%5D%2B5%2Ad=37%2Ca%5B1%5D%2B9%2Ad=53%29 ALIGN=MIDDLE  ALT=\"system%28a%5B1%5D%2B5%2Ad=37%2Ca%5B1%5D%2B9%2Ad=53%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is solved to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28highlight%28a%5B1%5D=17%29%2Cd=4%29 ALIGN=MIDDLE  ALT=\"system%28highlight%28a%5B1%5D=17%29%2Cd=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );