document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185789>Question 1185789</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of each of these series using the series formula.\r<BR>\n" );
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document.write( "a)  -11 - 3 + 5 + 13 + ... + 125\r<BR>\n" );
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document.write( "b)  6 - 18 + 54 - ... + 39366 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816626 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52943)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Find the sum of each of these series using the series formula.<BR>\n" );
document.write( "a) -11 - 3 + 5 + 13 + ... + 125<BR>\n" );
document.write( "b) 6 - 18 + 54 - ... + 39366<BR>\n" );
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document.write( "Arithmetic progression with the first term of -11;  the last term of 125, and the common difference of 8.  \r\n" );
document.write( "The number of terms n is\r\n" );
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document.write( "    n = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28125+-+%28-11%29%29%2F8 ALIGN=MIDDLE  ALT=\"%28125+-+%28-11%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28125%2B11%29%2F8 ALIGN=MIDDLE  ALT=\"%28125%2B11%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136%2F8 ALIGN=MIDDLE  ALT=\"136%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1 = 17 + 1 = 18.\r\n" );
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document.write( "(the difference of the last term and the first term, divided by the common difference, PLUS 1).\r\n" );
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document.write( "Apply the formula for the sum of the first n terms of an arithmetic progression\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D ALIGN=MIDDLE  ALT=\"S%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An ALIGN=MIDDLE  ALT=\"%28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-11%2B125%29%2F2%29%2A18 ALIGN=MIDDLE  ALT=\"%28%28-11%2B125%29%2F2%29%2A18\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28114%2F2%29%2A18 ALIGN=MIDDLE  ALT=\"%28114%2F2%29%2A18\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 57*18 = 1026.     <U>ANSWER</U>\r\n" );
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document.write( "Part &nbsp;(a) &nbsp;is solved.\r<BR>\n" );
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document.write( "Solve part &nbsp;(b) &nbsp;PRECISELY &nbsp;in the same way, using my instructions.\r<BR>\n" );
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document.write( "For introductory lessons on arithmetic progressions see \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic <U>\"Arithmetic progressions\"</U>.\r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( "////////////\r<BR>\n" );
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document.write( "You are a lucky person (!)\r<BR>\n" );
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document.write( "You have one problem solved for you by the tutor, &nbsp;and you have the second problem \r<BR>\n" );
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document.write( "to solve &nbsp;ON &nbsp;YOUR &nbsp;OWN &nbsp;having a &nbsp;TEMPLATE &nbsp;and following given instructions.\r<BR>\n" );
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document.write( "So, &nbsp;you can check yourself if you do understand the subject.\r<BR>\n" );
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document.write( "In addition, &nbsp;you have lessons to learn everything from there . . . \r<BR>\n" );
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document.write( "Happy learning &nbsp;(&nbsp;!&nbsp;)\r<BR>\n" );
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document.write( "Do not forget to post your &nbsp;\" THANKS \" &nbsp;to me for my teaching &nbsp;(&nbsp;!&nbsp;)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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