document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169187>Question 1169187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first and 4th term of a G.P is -1575 while the sum of the 3rd and 6th term is -25200. Find the first term, common ratio, and the sum of the 4th to 20th term inclusive. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793813 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=793813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "a, ar, ar^2, ar^3, ar^4, ar^5, ar^6, ...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar%5E3+=+-1575 ALIGN=MIDDLE  ALT=\"a%2Bar%5E3+=+-1575\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The sum of the 1st and 4th terms is -1575<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2%2Bar%5E5+=+-25200 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bar%5E5+=+-25200\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The sum of the 3rd and 6th terms is -25200<br><BR>\n" );
document.write( "Factor out the common term a^2 in the second equation.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%28a%2Bar%5E3%29+=+r%5E2%28-1575%29+=+-25200 ALIGN=MIDDLE  ALT=\"r%5E2%28a%2Bar%5E3%29+=+r%5E2%28-1575%29+=+-25200\"   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+=+-25200%2F-1575+=+16 ALIGN=MIDDLE  ALT=\"r%5E2+=+-25200%2F-1575+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The common ratio r is either 4 or -4.<br><BR>\n" );
document.write( "Suppose r=4.  Then the sum of the 1st and 4th terms is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar%5E3+=+a%2B64a+=+65a+=+-1575 ALIGN=MIDDLE  ALT=\"a%2Bar%5E3+=+a%2B64a+=+65a+=+-1575\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That gives a non-integer value for the first term a.<br><BR>\n" );
document.write( "So let's try r=-4.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar%5E3+=+a-64a+=+-63a+=+-1575 ALIGN=MIDDLE  ALT=\"a%2Bar%5E3+=+a-64a+=+-63a+=+-1575\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-1575%2F-63+=+25 ALIGN=MIDDLE  ALT=\"a+=+-1575%2F-63+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The first term is a=25; the common ratio is a=-4.<br><BR>\n" );
document.write( "The first few terms are<br><BR>\n" );
document.write( "25, -100, 400, -1600, 6400, -25600, ....<br><BR>\n" );
document.write( "To find the sum of the 4th through 20th terms, find the sum of the first 20 terms and subtract the sum of the first 3 terms.<br><BR>\n" );
document.write( "The 20th term of the sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28-4%29%5E19 ALIGN=MIDDLE  ALT=\"25%28-4%29%5E19\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is about -6.87x10^12, so you will need a calculator that can handle large numbers if you need to get an exact answer.  An excel spreadsheet is one option that will work nicely.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );