document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141683>Question 1141683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The twenty first term of an app is five and a half while the sum of the twenty one terms is ninetyfour and a half.find the sum of the first 3 terms of the ap </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762272 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula for nth term of an arithmetic progression is An = A1 + (n-1) * d           \r<BR>\n" );
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document.write( "formula for sum of n terms of an arithmetic progression is Sn = n * (A1 + An) / 2\r<BR>\n" );
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document.write( "you are given that the 21st term of an arithmetic progression is equal to 5.5.\r<BR>\n" );
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document.write( "you are also given that the sum of the first 21 terms of the arithmetic progression is 94.5.\r<BR>\n" );
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document.write( "since Sn = n * (A1 + An) / 2, then you get 94.5 = 21 * (A1 + 5.5) / 2.\r<BR>\n" );
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document.write( "simplify the equation to get 94.5 = (21 * A1 + 115.5) / 2\r<BR>\n" );
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document.write( "multiply both sides of that equation by 2 to get 189 = 21 * A1 + 115.5\r<BR>\n" );
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document.write( "subtract 115.5 from both sides of that equation to get 73.5 = 21 * A1\r<BR>\n" );
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document.write( "divide both sides of that equation by 21 to get 3.5 = A1.\r<BR>\n" );
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document.write( "since An = A1 + (n-1) * d, then A21 = A1 + 20 * d.\r<BR>\n" );
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document.write( "since A21 = 5.5 and A1 = 3.5, then 5.5 = 3.5 + 20 * d\r<BR>\n" );
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document.write( "subtract 3.5 from both sides of that equation to get 2 = 20 * d.\r<BR>\n" );
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document.write( "divide both sides of that equation by 20 to get 2 / 20 = d.\r<BR>\n" );
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document.write( "solve for d to get d = .1\r<BR>\n" );
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document.write( "you have A1 = 3.5 and d = .1\r<BR>\n" );
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document.write( "you want the sum of the first 3 terms of the arithmetic progression.\r<BR>\n" );
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document.write( "A1 = 3.5<BR>\n" );
document.write( "A2 = 3.5 + 1 * .1 = 3.6<BR>\n" );
document.write( "A3 = 3.5 + 2 * .1 = 3.7\r<BR>\n" );
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document.write( "since it's only 3 terms, you can just add them up.\r<BR>\n" );
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document.write( "sum of the first 3 terms is 3.5 + 3.6 + 3.7 = 10.8.\r<BR>\n" );
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document.write( "you can also use the sum of an arithmetic progression formula to get S3 = 3 * (A1 + A3) / 2 = 3 * (3.5 + 3.7) / 2 = 3 * 7.2 / 2 = 3 * 3.6 = 10.8.\r<BR>\n" );
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document.write( "your solution is that the sum of the first 3 terms of the arithmetic progression is 10.8.\r<BR>\n" );
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