document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106491>Question 1106491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the arithmetic series, if S_n = 5n^2+4n, find the first three terms.\r<BR>\n" );
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document.write( "So the first term is 9, and I tried using the formula S_n= (a1+an)/2 * n\r<BR>\n" );
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document.write( "I got confused... does an = 5n^2+4n </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721490 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=721490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The sum of n terms of an arithmetic series is<br><BR>\n" );
document.write( "(number of terms) times (average of first and last terms)<br><BR>\n" );
document.write( "If the first term is a and the common difference is d, then the sum of the first and last terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+a%2B%28n-1%29d+=+2a%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"a+%2B+a%2B%28n-1%29d+=+2a%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the sum of the first n terms is then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28%282a%2B%28n-1%29d%29%2F2%29 ALIGN=MIDDLE  ALT=\"n%28%282a%2B%28n-1%29d%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We are told that the sum of the first n terms of the sequence is 5n^2+4n.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28%282a%2B%28n-1%29d%29%2F2%29+=+5n%5E2%2B4n ALIGN=MIDDLE  ALT=\"n%28%282a%2B%28n-1%29d%29%2F2%29+=+5n%5E2%2B4n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%282a%2Bdn-d%29+=+10n%5E2%2B8n ALIGN=MIDDLE  ALT=\"n%282a%2Bdn-d%29+=+10n%5E2%2B8n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dn+%2B+%282a-d%29+=+10n%2B8 ALIGN=MIDDLE  ALT=\"dn+%2B+%282a-d%29+=+10n%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This tells us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dn+=+10n ALIGN=MIDDLE  ALT=\"dn+=+10n\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means d is 10, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a-d+=+8 ALIGN=MIDDLE  ALT=\"2a-d+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a-10+=+8 ALIGN=MIDDLE  ALT=\"2a-10+=+8\"   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( "So the arithmetic series has first term 9 and common difference 10.<br><BR>\n" );
document.write( "Then the first three terms are 9, 19, and 29. </SPAN>\n" );
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