document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39195>Question 39195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Still do not understand. Please help again.\r<BR>\n" );
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document.write( "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( "Show work in this space.   \r<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:  \r<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 #24633 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=24633\">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( "r is the number which is used to multiply a term of the sequence to <BR>\n" );
document.write( "get the following term of the sequence.  So to determine \"r\" you need<BR>\n" );
document.write( "to divide any term of the sequence by the term immediately preceding it.<BR>\n" );
document.write( "For example, divide the 2nd term by the 1st term to get the following:<BR>\n" );
document.write( "r = [1/3]/1= 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" );
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document.write( "Show work in this space. <BR>\n" );
document.write( "The formula for the sum of \"n\" terms is as follows:<BR>\n" );
document.write( "S(n)=a(1)[r^n-1]/[r-1]<BR>\n" );
document.write( "a(1)=1 in your problem<BR>\n" );
document.write( "So, the sum of the first 10 terms is as follows:<BR>\n" );
document.write( "S(10)=1[r^10-1]/[r-1]= [(1/3)^10-1]/[1/3 - 1]<BR>\n" );
document.write( "=-0.99998306.../(-2/3)1.49997460... \r<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" );
document.write( "Show work in this space.<BR>\n" );
document.write( "Similarly the sum of the first 12 terms is as follows: \r<BR>\n" );
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document.write( "S(12)=1[(1/3)^12 - 1]/[(1/3)-1]= -0.99999812.../(-2/3)<BR>\n" );
document.write( "=1.49999718... \r<BR>\n" );
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document.write( "d) What observation can you make about these sums? In particular, what number does it appear that the sum will always be smaller than?<BR>\n" );
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document.write( "As you take more and more terms the sum of the sequence of terms<BR>\n" );
document.write( "gets closer and closer to 1.5\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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