document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154630>Question 1154630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The third term of a geometric sequence is 12 and <BR>\n" );
document.write( "the fifth term is 16/3.<BR>\n" );
document.write( "Determine the formula for a⬇️n, nth term of this sequence.<BR>\n" );
document.write( "Find the value of a⬇️25. (25 is beneath a and n is beneath a as well)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777097 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The 5th term is the 3rd term, multiplied by the common ratio 2 times:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3+=+12%28r%5E2%29 ALIGN=MIDDLE  ALT=\"16%2F3+=+12%28r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+%2816%2F3%29%2F12+=+16%2F36+=+4%2F9 ALIGN=MIDDLE  ALT=\"r%5E2+=+%2816%2F3%29%2F12+=+16%2F36+=+4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+2%2F3 ALIGN=MIDDLE  ALT=\"r+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+-2%2F3 ALIGN=MIDDLE  ALT=\"r+-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We can write a formula for the nth term of the sequence using any known term; it is not necessary to find the first term.  I will use the given 3rd term.<br><BR>\n" );
document.write( "Since there are two possible values for the common ratio, there are different possible formulas for the n-th term.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28n%29+=+12%28%282%2F3%29%5E%28n-3%29%29 ALIGN=MIDDLE  ALT=\"t%28n%29+=+12%28%282%2F3%29%5E%28n-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28n%29+=+12%28%28-2%2F3%29%5E%28n-3%29%29 ALIGN=MIDDLE  ALT=\"t%28n%29+=+12%28%28-2%2F3%29%5E%28n-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The 25th term will be the same using either formula, because the exponent will be even.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2825%29+=+12%28%282%2F3%29%5E22%29 ALIGN=MIDDLE  ALT=\"t%2825%29+=+12%28%282%2F3%29%5E22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use a calculator....<br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );