document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185343>Question 1185343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please check the document for the question: \r<BR>\n" );
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document.write( "https://docs.google.com/document/d/1Cl3HrcoR6jibNzxfDTIilS3imSplLY8nQUU0OpU9vLA/edit?usp=sharing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816152 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=816152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this looks like an arithmetic sequence type problem.\r<BR>\n" );
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document.write( "in an arithmetic sequence An = A1 + (n-1) * d\r<BR>\n" );
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document.write( "if d = 4, then An = A1 + (n-1) * 4\r<BR>\n" );
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document.write( "A2 would be equal to A1 + 1 * 4 which is equal to A1 + 4.\r<BR>\n" );
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document.write( "if A1 is equal to 10, then A2 would be equal to 14.\r<BR>\n" );
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document.write( "A3 would be equal to 10 + 2 * 4 = 18 which is also equal to A2 + 4\r<BR>\n" );
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document.write( "A4 would be equal to 10 + 3 * 4 = 22 which is also equal to A3 + 4\r<BR>\n" );
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document.write( "what this is saying is that An+1 is always equal to An + 4.\r<BR>\n" );
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document.write( "A20 would be equal to 10 + 19 * 4 = 10 + 76 = 86\r<BR>\n" );
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document.write( "the sum of an arithmetic sequence is equal to n/2 * (A1 + An).\r<BR>\n" );
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document.write( "since An = A1 + (n-1) * d, this formula can also be expressed as:\r<BR>\n" );
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document.write( "sum = n/2 * (A1 + A1 + (n-1) * d).\r<BR>\n" );
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document.write( "this becomes sum = n/2 * (2 * A1 + (n-1) * d).\r<BR>\n" );
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document.write( "either way, you'll get the sum.\r<BR>\n" );
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document.write( "if sum = n/2 * (A1 + An), you first have to find An.\r<BR>\n" );
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document.write( "when n = 20 and A1 = 10 and d = 4, A20 = 10 + 19 * 4 =  10 + 76 = 86.\r<BR>\n" );
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document.write( "sum is then equal to 20/2 * 10 + 86) = 10 * 96 = 960.\r<BR>\n" );
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document.write( "if sum = n/2 * (2 * A1 + (n-1) * d), then:\r<BR>\n" );
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document.write( "sum = 20/2 * (2 * 10 + 19 * 4) which becomes equal to 10 * (20 + 76) which is equal to 10 * 96 which is equal to 960.\r<BR>\n" );
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document.write( "the two formulas get you the same answer.\r<BR>\n" );
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document.write( "if you simply did the sum manually, you would get:\r<BR>\n" );
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document.write( "A1 = 10<BR>\n" );
document.write( "A2 = 14<BR>\n" );
document.write( "A3 = 18<BR>\n" );
document.write( "A4 = 22<BR>\n" );
document.write( "A5 = 26<BR>\n" );
document.write( "A6 = 30<BR>\n" );
document.write( "A7 = 34<BR>\n" );
document.write( "A8 = 38<BR>\n" );
document.write( "A9 = 42<BR>\n" );
document.write( "A10 = 46<BR>\n" );
document.write( "A11 = 50<BR>\n" );
document.write( "A12 = 54<BR>\n" );
document.write( "A13 = 58<BR>\n" );
document.write( "A14 = 62<BR>\n" );
document.write( "A15 = 66<BR>\n" );
document.write( "A16 = 70<BR>\n" );
document.write( "A17 = 74<BR>\n" );
document.write( "A18 = 78<BR>\n" );
document.write( "A19 = 82<BR>\n" );
document.write( "A20 = 86\r<BR>\n" );
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document.write( "add those up and you get 960.\r<BR>\n" );
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