document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53621>Question 53621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time figuring out this problem.\r<BR>\n" );
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document.write( "Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:<BR>\n" );
document.write( "a) 	What is r, the ratio between 2 consecutive terms? \r<BR>\n" );
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document.write( "b) 	Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.<BR>\n" );
document.write( "c) 	Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.\r<BR>\n" );
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document.write( "Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35883 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Geometric Sequence: {1,1/2,1/4,1/8...}<BR>\n" );
document.write( "a)r=a(sub n+1)/a(sub n)  in some books r=a(sub n)/a(sub n-1).  It's the same thing, divide the 2nd term by the 1st, the 3rd by the 2nd, ect.<BR>\n" );
document.write( "r=(1/2)/(1)=1/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "r=(1/4)/(1/2)<BR>\n" );
document.write( "r=(1/4)*(2/1)<BR>\n" );
document.write( "r=2/4=1/2 <BR>\n" );
document.write( "---<BR>\n" );
document.write( "r=(1/8)/(1/4)<BR>\n" );
document.write( "r=(1/8)*(4/1)<BR>\n" );
document.write( "r=4/8=1/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Notice that in geometric sequences, you will get the same ratio with any two consecutive terms, in this case:r=1/2.<BR>\n" );
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document.write( "b)The sum of the first n terms is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+n%29=a%28sub+1%29%2A%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S%28sub+n%29=a%28sub+1%29%2A%281-r%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case you want the sum of the first 10 terms.<BR>\n" );
document.write( "n=10<BR>\n" );
document.write( "r=1/2<BR>\n" );
document.write( "The first term, a(sub 1)=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+10%29=1%2A%281-%281%2F2%29%5E10%29%2F%281-1%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+10%29=1%2A%281-%281%2F2%29%5E10%29%2F%281-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+10%29=%281-1%2F1024%29%2F%281-1%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+10%29=%281-1%2F1024%29%2F%281-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+10%29=%281024%2F1024-1%2F1024%29%2F%282%2F2-1%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+10%29=%281024%2F1024-1%2F1024%29%2F%282%2F2-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+10%29=%281023%2F1024%29%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+10%29=%281023%2F1024%29%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+10%29=%281023%2F1024%29%2A%282%2F1%29 ALIGN=MIDDLE  ALT=\"S%28sub+10%29=%281023%2F1024%29%2A%282%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+10%29=1023%2F512 ALIGN=MIDDLE  ALT=\"S%28sub+10%29=1023%2F512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S(sub 10)=1.9980<BR>\n" );
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document.write( "c)  This time<BR>\n" );
document.write( "n=12<BR>\n" );
document.write( "r=1/2<BR>\n" );
document.write( "a(sub 1)=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+n%29=a%28sub+1%29%2A%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S%28sub+n%29=a%28sub+1%29%2A%281-r%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+12%29=1%2A%281-%281%2F2%29%5E12%29%2F%281-1%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+12%29=1%2A%281-%281%2F2%29%5E12%29%2F%281-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+12%29=%281-1%2F4096%29%2F%281-1%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+12%29=%281-1%2F4096%29%2F%281-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+12%29=%284096%2F4096-1%2F4096%29%2F%282%2F2-1%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+12%29=%284096%2F4096-1%2F4096%29%2F%282%2F2-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+12%29=%284095%2F4096%29%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"S%28sub+12%29=%284095%2F4096%29%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+12%29=%284095%2F4096%29%2A%282%2F1%29 ALIGN=MIDDLE  ALT=\"S%28sub+12%29=%284095%2F4096%29%2A%282%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+12%29=4095%2F2048 ALIGN=MIDDLE  ALT=\"S%28sub+12%29=4095%2F2048\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S(sub 12)=1.9995<BR>\n" );
document.write( "Happy Calculating! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );