document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092302>Question 1092302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Sum of first 20th terms is 200 and Sum of next 10 terms is 400.What is the 40th term? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706926 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=706926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>You don't say so, but I will assume this is an arithmetic sequence....<br><BR>\n" );
document.write( "In any arithmetic sequence, the sum of n terms is n times the average of the first and last terms.<br><BR>\n" );
document.write( "The sum of the first 20 terms is 20 times the average of the first and 20th terms.  If the first term is a and the common difference is d, then the 20th term is a+19d.  Since your problem says the sum of the first 20 terms is 200,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%28a%2B%28a%2B19d%29%29%2F2+=+200 ALIGN=MIDDLE  ALT=\"20%28a%2B%28a%2B19d%29%29%2F2+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%282a%2B19d%29+=+200 ALIGN=MIDDLE  ALT=\"10%282a%2B19d%29+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B19d+=+20 ALIGN=MIDDLE  ALT=\"2a%2B19d+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (1)<br><BR>\n" );
document.write( "Also in your problem the sum of the next 10 terms (terms 21 through 30) is 400.  The 21st term is a+20d; the 30th is a+29d.  The sum of those 10 terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28%28a%2B20d%29%2B%28a%2B29d%29%29%2F2+=+400 ALIGN=MIDDLE  ALT=\"10%28%28a%2B20d%29%2B%28a%2B29d%29%29%2F2+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B49d+=+80 ALIGN=MIDDLE  ALT=\"2a%2B49d+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (2)<br><BR>\n" );
document.write( "Subtract equation (1) from equation (2) and solve for d; then plug that value for d in either (1) or (2) to solve for a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30d+=+60 ALIGN=MIDDLE  ALT=\"30d+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+2 ALIGN=MIDDLE  ALT=\"d+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B19%282%29+=+20 ALIGN=MIDDLE  ALT=\"2a%2B19%282%29+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B38+=+20 ALIGN=MIDDLE  ALT=\"2a%2B38+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a+=+-18 ALIGN=MIDDLE  ALT=\"2a+=+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-9 ALIGN=MIDDLE  ALT=\"a+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We are to find the 40th term, which is a+39d:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2B40%282%29+=+-9%2B80+=+71 ALIGN=MIDDLE  ALT=\"-9%2B40%282%29+=+-9%2B80+=+71\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The 40th term is 71.<br><BR>\n" );
document.write( "Oops!  I said the 40th term is a+39d, but then I calculated a+40d.<br><BR>\n" );
document.write( "The 40th term is a+39d:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2B39%282%29+=+-9%2B78+=+69 ALIGN=MIDDLE  ALT=\"-9%2B39%282%29+=+-9%2B78+=+69\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the 40th term is 69, which is one of your answer choices.\r<BR>\n" );
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