document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047528>Question 1047528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first 30 terms of a geometric sequence is: <BR>\n" );
document.write( "18[1-(2/3)^30]<BR>\n" );
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document.write( "1/3\r<BR>\n" );
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document.write( "a. what are the first five terms of the sequence? \r<BR>\n" );
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document.write( "b. Estimate the sum of the first one million terms. (How do I do this?) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663058 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=663058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It's quite obvious from the fact <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B30%5D=+18%2A%28%281-%282%2F3%29%5E30%29%2F%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"S%5B30%5D=+18%2A%28%281-%282%2F3%29%5E30%29%2F%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+18%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+18%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and r = 2/3\r<BR>\n" );
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document.write( "a.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+18%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+18%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+12%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+12%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+8%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+8%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D+=+16%2F3%5D ALIGN=MIDDLE  ALT=\"a%5B4%5D+=+16%2F3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D+=+32%2F9%5D ALIGN=MIDDLE  ALT=\"a%5B5%5D+=+32%2F9%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "b.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1000000%5D+=+a%5B1%5D%2F%281-r%29+-+r%5E1000000%2F%281-r%29+=++18%2F%281-2%2F3%29+-+%282%2F3%29%5E1000000%2F%281-2%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since 0 < 2/3 < 1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%5E1000000%2F%281-2%2F3%29+=+3%2A%282%2F3%29%5E1000000 ALIGN=MIDDLE  ALT=\"%282%2F3%29%5E1000000%2F%281-2%2F3%29+=+3%2A%282%2F3%29%5E1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > is practically 0.\r<BR>\n" );
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document.write( "Thus an estimate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1000000%5D ALIGN=MIDDLE  ALT=\"S%5B1000000%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18%2F%281-2%2F3%29+=+54 ALIGN=MIDDLE  ALT=\"+18%2F%281-2%2F3%29+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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