document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38761>Question 38761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3)	Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following:<BR>\n" );
document.write( "a)	What is r, the ratio between 2 consecutive terms? <BR>\n" );
document.write( "Answer:  <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? Carry all calculations to 7 significant figures.<BR>\n" );
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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? Carry all calculations to 7 significant figures.<BR>\n" );
document.write( "Answer:  <BR>\n" );
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document.write( "d)	What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?<BR>\n" );
document.write( "Answer:  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24254 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=24254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3)	Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following:<BR>\n" );
document.write( "a)	What is r, the ratio between 2 consecutive terms? <BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "To do this, you take the second number and divide that by the first number.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2F1+=+1%2F3 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2F1+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The ratio is (1/3).\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? Carry all calculations to 7 significant figures.<BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space.   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28%28a%29%281-r%5E%28n%29%29%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"s+=+%28%28a%29%281-r%5E%28n%29%29%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+=+%28%281%29%281-%281%2F3%29%5E%2810%29%29%29%2F%281-%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"s+=+%28%281%29%281-%281%2F3%29%5E%2810%29%29%29%2F%281-%281%2F3%29%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+=+%2859048%2F59049%29%2F%282%2F3%29 ALIGN=MIDDLE  ALT=\"s+=+%2859048%2F59049%29%2F%282%2F3%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+=+29524%2F19683 ALIGN=MIDDLE  ALT=\"s+=+29524%2F19683\"   DISABLED_style= \"max-width:90%; height:auto;\" > about 1.499975<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? Carry all calculations to 7 significant figures.<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space.   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%281-%281%2F3%29%5E%2812%29%29%2F%281-%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"s+=+%281-%281%2F3%29%5E%2812%29%29%2F%281-%281%2F3%29%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+=+%28531440%2F531441%29%2F%282%2F3%29 ALIGN=MIDDLE  ALT=\"s+=+%28531440%2F531441%29%2F%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "about 1.499997\r<BR>\n" );
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document.write( "d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?<BR>\n" );
document.write( "Always smaller than 1.5 it seems. The number will increase very minimal as the number of terms added increases. </SPAN>\n" );
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