document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157839>Question 1157839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given two terms in a geometric sequence find the term named in the problem and the explicit formula\r<BR>\n" );
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document.write( "http://prntscr.com/s9icre </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780794 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=780794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "#24....<br><BR>\n" );
document.write( "For any geometric sequence,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28n%29+=+a%280%29%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%28n%29+=+a%280%29%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The formula says exactly what the definition of a geometric sequence says: the n-th term is the first term, multiplied by the common ratio, r, (n-1) times.<br><BR>\n" );
document.write( "Note it is (n-1) times, because the first term is multiplied by the common ratio 0 times.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%285%29=48 ALIGN=MIDDLE  ALT=\"a%285%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%284%29=24 ALIGN=MIDDLE  ALT=\"a%284%29=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Formally, divide a(5) by a(4):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%285%29%2Fa%284%29+=+%28a%280%29r%5E4%29%2F%28a%280%29r%5E3%29+=+r ALIGN=MIDDLE  ALT=\"a%285%29%2Fa%284%29+=+%28a%280%29r%5E4%29%2F%28a%280%29r%5E3%29+=+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+48%2F24+=+2 ALIGN=MIDDLE  ALT=\"r+=+48%2F24+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Informally, simply observe that the 5th term is the 4th term multiplied by the common ratio; 48/24 = 2.<br><BR>\n" );
document.write( "We have determined r; to finish finding the explicit formula, we need to find a(0).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%284%29+=+24+=+a%280%29r%5E3+=+a%280%292%5E3+=+8a%280%29 ALIGN=MIDDLE  ALT=\"a%284%29+=+24+=+a%280%29r%5E3+=+a%280%292%5E3+=+8a%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%280%29+=+24%2F8+=+3 ALIGN=MIDDLE  ALT=\"a%280%29+=+24%2F8+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The explicit formula is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28n%29+=+3%282%5E%28n-1%29%29 ALIGN=MIDDLE  ALT=\"a%28n%29+=+3%282%5E%28n-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Evaluate a(9) using the formula.<br><BR>\n" );
document.write( "Or, informally, multiply the 5th term, 48, by 2, 4 more times....<br><BR>\n" );
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