document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062748>Question 1062748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is my problem: There are two geometric sequences with 3rd term 5 and 5th term 80. What are the two possible values of the 4th term?\r<BR>\n" );
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document.write( "I have my two equations of <BR>\n" );
document.write( "5=ar^2<BR>\n" );
document.write( "80=ar^4<BR>\n" );
document.write( "(a is first term and r is mutliplier quantity)\r<BR>\n" );
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document.write( "I then go to 80/5 = r^4/r^2 which then ends up being 16r = r^2 and over to r^2 - 16r = 0. Completing the square gives me r^2 - 16r + 64 = 64. Problem is that then gets me right back to my pre-completing the square part. My other option is to do r(r-16) = 0 which gives me r = 0 and 16 which can't work because r = 0 doesn't give me any workable answer. So I must assume I'm doing something wrong. \r<BR>\n" );
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document.write( "Thanks for any help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677731 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=677731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You should go from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F5+=+r%5E4%2Fr%5E2 ALIGN=MIDDLE  ALT=\"80%2F5+=+r%5E4%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+r%5E2 ALIGN=MIDDLE  ALT=\"16+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving for r leads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+4 ALIGN=MIDDLE  ALT=\"r+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-4 ALIGN=MIDDLE  ALT=\"r+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is after you apply the square root to both sides. Don't forget to use the plus/minus.\r<BR>\n" );
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document.write( "Now that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+4 ALIGN=MIDDLE  ALT=\"r+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-4 ALIGN=MIDDLE  ALT=\"r+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can use this to find the fourth term\r<BR>\n" );
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document.write( "fourth term = r*(third term)<BR>\n" );
document.write( "fourth term = r*5\r<BR>\n" );
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document.write( "If r = 4, then<BR>\n" );
document.write( "fourth term = r*5<BR>\n" );
document.write( "fourth term = 4*5<BR>\n" );
document.write( "fourth term = 20\r<BR>\n" );
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document.write( "OR\r<BR>\n" );
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document.write( "If r = -4, then<BR>\n" );
document.write( "fourth term = r*5<BR>\n" );
document.write( "fourth term = -4*5<BR>\n" );
document.write( "fourth term = -20\r<BR>\n" );
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document.write( "Question: There are two geometric sequences with 3rd term 5 and 5th term 80. What are the two possible values of the 4th term?\r<BR>\n" );
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document.write( "Answer: <font color=red>20 or -20</font>\r<BR>\n" );
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