document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33818>Question 33818</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279085/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 1)Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:<BR>\n" );
document.write( "a)What is d, the difference between any 2 terms? <BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space.	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:	<BR>\n" );
document.write( "Show work in this space.	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? <BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?<BR>\n" );
document.write( "Answer:	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2)Use the geometric sequence of numbers 1, 2, 4, 8,…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.	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)	Using the formula for the nth term of a geometric sequence, what is the 24th term?<BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space.	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c)Using the formula for the sum of a geometric series, what is the sum of the first 10 terms? <BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3)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? <BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space.	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "Answer: <BR>\n" );
document.write( "Show work in this space.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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.<BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space. 	\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20207 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=20207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE ANSWERS BELOW<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "1)Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:<BR>\n" );
document.write( "a)What is d, the difference between any 2 terms? <BR>\n" );
document.write( "Answer: 2<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "3-1=5-3=...ETC...=2\r<BR>\n" );
document.write( "\n" );
document.write( "b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: T101=1+100*2=201<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "TN=A+(N-1)D....A=1....N=101......D=2\r<BR>\n" );
document.write( "\n" );
document.write( "c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? <BR>\n" );
document.write( "Answer: S20=(20/2){2*1+(20-1)2}=10*40=400<BR>\n" );
document.write( "Show work in this space <BR>\n" );
document.write( "SN=(N/2){2A+(N-1)D}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Answer: S30=15*60=900<BR>\n" );
document.write( "Show work in this space <BR>\n" );
document.write( "SAME AS ABOVE\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?<BR>\n" );
document.write( "Answer: SN=N^2<BR>\n" );
document.write( "SN=(N/2){2+(N-1)2}=N*2N/2=N^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2)Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:<BR>\n" );
document.write( "a)What is r, the ratio between 2 consecutive terms? <BR>\n" );
document.write( "Answer: 2<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "2/1=4/2=8/4=....ETC...=2<BR>\n" );
document.write( "b) Using the formula for the nth term of a geometric sequence, what is the 24th term?<BR>\n" );
document.write( "Answer: T24=1*{2^23)=2^23<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "TN=A*R^(N-1)<BR>\n" );
document.write( "c)Using the formula for the sum of a geometric series, what is the sum of the first 10 terms? <BR>\n" );
document.write( "Answer: S10=1*{2^10-1}<BR>\n" );
document.write( "Show work in this space <BR>\n" );
document.write( "SN=A*{R^N-1}/(R-1)....N=10...R=2....A=1<BR>\n" );
document.write( "3)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? <BR>\n" );
document.write( "Answer: 1/2<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "(1/2)/1=(1/4)/(1/2)=...ETC...1/2<BR>\n" );
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( "Answer: {1-(1/2)^10}/(1-1/2)<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "SN=A{1-R^N}/(R-1)<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.<BR>\n" );
document.write( "Answer: {1-(1/2)^12}/(1-1/2)<BR>\n" );
document.write( "Show work in this space. <BR>\n" );
document.write( "SAME AS ABOVE<BR>\n" );
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" );
document.write( "THE SUM APPROACHES 1/(1-1/2)=2 AS N INCREASE TO LARGE NUMBERS...\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );