document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=493683>Question 493683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the third and sixth terms of a geometric sequence are-75 and -9375 respectively. Find the first term, common ratio, and an explict rule for the nth term. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335423 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=335423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the third and sixth terms of a geometric sequence are-75 and -9375 respectively. Find the first term, common ratio, and an explict rule for the nth term.<BR>\n" );
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document.write( "The general formula for the n-th term of a geometric sequence is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a_n+=+a%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a_n+=+a%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where a = the 1st term, r = the common ratio<BR>\n" );
document.write( "Given: a_3 = -75, a_6 = -9375<BR>\n" );
document.write( "So we have two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a_3+=+-75+=+a%2Ar%5E2 ALIGN=MIDDLE  ALT=\"a_3+=+-75+=+a%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a_6+=+-9375+=+a%2Ar%5E5 ALIGN=MIDDLE  ALT=\"a_6+=+-9375+=+a%2Ar%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the 1st equation we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-75%2Fr%5E2 ALIGN=MIDDLE  ALT=\"a+=+-75%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting this into the equation for a_6 gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9375+=+%28-75%2Fr%5E2%29%2Ar%5E5 ALIGN=MIDDLE  ALT=\"-9375+=+%28-75%2Fr%5E2%29%2Ar%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3+=+125 ALIGN=MIDDLE  ALT=\"r%5E3+=+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This gives r = 5<BR>\n" );
document.write( "Use the formula for a_3 above to solve for a:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-75+=+a%2A5%5E2 ALIGN=MIDDLE  ALT=\"-75+=+a%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This gives a = -3<BR>\n" );
document.write( "So the rule for the nth term is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a_n+=+-3%2A5%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a_n+=+-3%2A5%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );