document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252350>Question 252350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For certain arithmetic sequence, S 21= 546, S 22= 660 and d=8; determine S 23. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184273 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, we start with three formulas:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Tn+=+A1+%2B+8%28n-1%29 ALIGN=MIDDLE  ALT=\"Tn+=+A1+%2B+8%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This gives us the nth term of the arithmetic sequence.\r<BR>\n" );
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document.write( "SUM(n=1 to K) (constant) = K*constant\r<BR>\n" );
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document.write( "SUM(n=1 to k)(n) = k(k+1)/2.\r<BR>\n" );
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document.write( "We want SUM(n=1 to k) {A1 + 8n - 8}\r<BR>\n" );
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document.write( "this can be expressed as\r<BR>\n" );
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document.write( "SUM(n=1 to k) {A1} + SUM(n=1 to k) {8n} - SUM(n=1 to k) {8}\r<BR>\n" );
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document.write( "This gives us kA1 + 8(k)(K+1)/2 - 8k\r<BR>\n" );
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document.write( "Now<BR>\n" );
document.write( "S21 = 21A1 + 4(21)(22) - 8(21) = 546<BR>\n" );
document.write( "S22 = 22A1 + 4(22)(23) - 8(22) = 660\r<BR>\n" );
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document.write( "Subtracting the first from the second, we get\r<BR>\n" );
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document.write( "A1 + 176 - 8 = 114\r<BR>\n" );
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document.write( "A1 = -54.\r<BR>\n" );
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document.write( "Now, we have the formula for Tn as\r<BR>\n" );
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document.write( "Tn = -54 + 8(n-1)\r<BR>\n" );
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document.write( "The sum of the first 23 terms can be expressed as\r<BR>\n" );
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document.write( "SUM(n=1 to 23) {-54 + 8n - 8}\r<BR>\n" );
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document.write( "SUM(n=1 to 23) {-54} + SUM(n=1 to 23) {8n} - SUM(n=1 to 23) {8}\r<BR>\n" );
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document.write( "-54*23 + 8(23)(24)/2 - 8(23)\r<BR>\n" );
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document.write( "-1242 + 2208 -184 = 782.\r<BR>\n" );
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document.write( "S23 = 782. </SPAN>\n" );
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