document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092202>Question 1092202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first two terms of a geometric series is 90. The third term is 24.\r<BR>\n" );
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document.write( "A. Show That there are two possible series and find the term and the common ration in each case.\r<BR>\n" );
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document.write( "B. Show that both series converge and find their respective sums. </SPAN>\n" );
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document.write( "The third term is 24:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2=24 ALIGN=MIDDLE  ALT=\"ar%5E2=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+24%2Fr%5E2 ALIGN=MIDDLE  ALT=\"a+=+24%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (1)<br><BR>\n" );
document.write( "The sum of the first two terms is 90:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bar+=+a%281%2Br%29+=+90 ALIGN=MIDDLE  ALT=\"a%2Bar+=+a%281%2Br%29+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (2)<br><BR>\n" );
document.write( "Substitute (1) into (2):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824%2Fr%5E2%29%281%2Br%29+=+90 ALIGN=MIDDLE  ALT=\"%2824%2Fr%5E2%29%281%2Br%29+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%281%2Br%29+=+90r%5E2 ALIGN=MIDDLE  ALT=\"24%281%2Br%29+=+90r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90r%5E2-24r-24+=+0 ALIGN=MIDDLE  ALT=\"90r%5E2-24r-24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15r%5E2-4r-4+=+0 ALIGN=MIDDLE  ALT=\"15r%5E2-4r-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285r%2B2%29%283r-2%29+=+0 ALIGN=MIDDLE  ALT=\"%285r%2B2%29%283r-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The two values of the common ratio are -2/5 and 2/3.<br><BR>\n" );
document.write( "For the common ratio -2/5, the first term a is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F%28-2%2F5%29%5E2+=+24%2F%284%2F25%29+=+150 ALIGN=MIDDLE  ALT=\"24%2F%28-2%2F5%29%5E2+=+24%2F%284%2F25%29+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That gives us the sequence 150, -60, 24, ...<br><BR>\n" );
document.write( "For the common ratio 2/3, the first term a is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F%282%2F3%29%5E2+=+24%2F%284%2F9%29+=+54 ALIGN=MIDDLE  ALT=\"24%2F%282%2F3%29%5E2+=+24%2F%284%2F9%29+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That gives us the sequence 54, 36, 24, ...<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );