document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003636>Question 1003636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following sequences are arithmetic?<BR>\n" );
document.write( "Select one or more:<BR>\n" );
document.write( "A. 1, -2, 4, -8, 16,-32,...<BR>\n" );
document.write( "B. 20, 12, 4, -4, -12, ...<BR>\n" );
document.write( "C. 1, 2, 4, 7, 11, ...<BR>\n" );
document.write( "D. -10, -5, 1, 8, 16,...<BR>\n" );
document.write( "E. 9.3, 9.9, 10.5, 11.1, 11.7,..\r<BR>\n" );
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document.write( "How many terms of the sequence 2, 4, 6, 8, 10,... yield a sum of 132? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620301 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52847)</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=620301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1) Which of the following sequences are arithmetic?<BR>\n" );
document.write( "Select one or more:<BR>\n" );
document.write( "A. 1, -2, 4, -8, 16,-32,...<BR>\n" );
document.write( "B. 20, 12, 4, -4, -12, ...<BR>\n" );
document.write( "C. 1, 2, 4, 7, 11, ...<BR>\n" );
document.write( "D. -10, -5, 1, 8, 16,...<BR>\n" );
document.write( "E. 9.3, 9.9, 10.5, 11.1, 11.7,..<BR>\n" );
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document.write( "B) &nbsp;and &nbsp;E)<BR>\n" );
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document.write( "2) &nbsp;How many terms of the sequence &nbsp;2, 4, 6, 8, 10,. . . &nbsp;yield a sum of &nbsp;132?\r<BR>\n" );
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document.write( "It is the arithmetic progression with the first term &nbsp;2 &nbsp;and the common difference &nbsp;2. \r<BR>\n" );
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document.write( "The formula for the sum of &nbsp;n &nbsp;first terms of an arithmetic progression is\r<BR>\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=%28a%5B1%5D+%2B+%28%28n-1%29%2Ad%29%2F2%29%2An ALIGN=MIDDLE  ALT=\"%28a%5B1%5D+%2B+%28%28n-1%29%2Ad%29%2F2%29%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(see the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>&nbsp; in this site). \r<BR>\n" );
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document.write( "In this case &nbsp;<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=%282+%2B+%28%28n-1%29%2A2%29%2F2%29%2An ALIGN=MIDDLE  ALT=\"%282+%2B+%28%28n-1%29%2A2%29%2F2%29%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n+%2B+n%2A%28n-1%29 ALIGN=MIDDLE  ALT=\"2n+%2B+n%2A%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therefore, &nbsp;to find &nbsp;n, &nbsp;we need to solve an equation \r<BR>\n" );
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document.write( "2n + n*(n-1) = 132.\r<BR>\n" );
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document.write( "Simplify and solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n ALIGN=MIDDLE  ALT=\"2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=132 ALIGN=MIDDLE  ALT=\"132\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=132 ALIGN=MIDDLE  ALT=\"132\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "Factor:\r<BR>\n" );
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document.write( "(n-11)*(n+12) = 0,\r<BR>\n" );
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document.write( "The roots are &nbsp;n = 11 &nbsp;and &nbsp;n = -12.\r<BR>\n" );
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document.write( "Only &nbsp;n = 11 &nbsp;does suit.\r<BR>\n" );
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document.write( "<U>Answer</U>. &nbsp;n = 11.\r<BR>\n" );
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