document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156304>Question 1156304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sum of a geometric series is 46.5. The first term of the series is 24​, and its common ratio is 0.5. How many terms are there in the​ series? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779001 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "n = number of terms = unknown<BR>\n" );
document.write( "S = 46.5 = sum of the first n terms<BR>\n" );
document.write( "a = 24 = first term<BR>\n" );
document.write( "r = 0.5 = common ratio\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%28a%281-r%5En%29%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S+=+%28a%281-r%5En%29%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Formula used to add the first n terms of a geometric sequence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46.5+=+%2824%281-0.5%5En%29%29%2F%281-0.5%29 ALIGN=MIDDLE  ALT=\"46.5+=+%2824%281-0.5%5En%29%29%2F%281-0.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46.5+=+%2824%281-0.5%5En%29%29%2F0.5 ALIGN=MIDDLE  ALT=\"46.5+=+%2824%281-0.5%5En%29%29%2F0.5\"   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=46.5%2A0.5+=+24%281-0.5%5En%29 ALIGN=MIDDLE  ALT=\"46.5%2A0.5+=+24%281-0.5%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 0.5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23.25+=+24%281-0.5%5En%29 ALIGN=MIDDLE  ALT=\"23.25+=+24%281-0.5%5En%29\"   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=24%281-0.5%5En%29+=+23.25 ALIGN=MIDDLE  ALT=\"24%281-0.5%5En%29+=+23.25\"   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=1-0.5%5En+=+23.25%2F24 ALIGN=MIDDLE  ALT=\"1-0.5%5En+=+23.25%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.5%5En+=+0.96875 ALIGN=MIDDLE  ALT=\"1-0.5%5En+=+0.96875\"   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=0.5%5En+=+1-0.96875 ALIGN=MIDDLE  ALT=\"0.5%5En+=+1-0.96875\"   DISABLED_style= \"max-width:90%; height:auto;\" > Isolate the term 0.5^n\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%5En+=+0.03125 ALIGN=MIDDLE  ALT=\"0.5%5En+=+0.03125\"   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=log%28%280.5%5En%29%29+=+log%28%280.03125%29%29 ALIGN=MIDDLE  ALT=\"log%28%280.5%5En%29%29+=+log%28%280.03125%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply logs to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%28%280.5%29%29+=+log%28%280.03125%29%29 ALIGN=MIDDLE  ALT=\"n%2Alog%28%280.5%29%29+=+log%28%280.03125%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > We do so to be able to pull the exponent n down. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+log%28%280.03125%29%29%2Flog%28%280.5%29%29 ALIGN=MIDDLE  ALT=\"n+=+log%28%280.03125%29%29%2Flog%28%280.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by log(0.5)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+5 ALIGN=MIDDLE  ALT=\"n+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a calculator\r<BR>\n" );
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document.write( "Answer: <font color=red>5 terms</font>\r<BR>\n" );
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document.write( "The first five terms are: {24, 12, 6, 3, 1.5}<BR>\n" );
document.write( "Each new term is found by multiplying the previous term by the common ratio 0.5\r<BR>\n" );
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document.write( "Those five terms add to<BR>\n" );
document.write( "24 + 12 + 6 + 3 + 1.5 = 46.5<BR>\n" );
document.write( "which confirms our answer. <BR>\n" );
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