document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83716>Question 83716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We are having a lecture this afternoon and I would like to be able to apply the lecture to this so that I can understand it.  Thanks for any help.\r<BR>\n" );
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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 two consecutive terms? <BR>\n" );
document.write( "Answer: <BR>\n" );
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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" );
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document.write( "c) 	Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms? <BR>\n" );
document.write( "Answer:	<BR>\n" );
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document.write( "d) 	Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Answer:	<BR>\n" );
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document.write( "e) 	What observation can you make about these sums of this sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?  Express your observations as a general formula in \"n.\"<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 #60205 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=60205\">put this solution on YOUR website!</A><BR><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 two consecutive terms? <BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space<BR>\n" );
document.write( "d is the difference between any term and its previous term<BR>\n" );
document.write( "d=3-1 = 2<BR>\n" );
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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" );
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document.write( "nth term = a(n) = a(1)+(n-1)d<BR>\n" );
document.write( "a(101) = 1 + 100*2 = 201<BR>\n" );
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document.write( "c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms? <BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space <BR>\n" );
document.write( "S(n) = (n/2)(a(1)+a(n))<BR>\n" );
document.write( "S(20) = (20/2)( 1 + a(20))\r<BR>\n" );
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document.write( "S(20) = 10(1+1+19*2)<BR>\n" );
document.write( "S(20 = 10(40) = 400<BR>\n" );
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document.write( "d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space <BR>\n" );
document.write( "S(30) = 15(1+1+29*2)<BR>\n" );
document.write( "S(30) = 15(60) = 900<BR>\n" );
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document.write( "e) What observation can you make about these sums of this sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in \"n.\"<BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "The sums are obviously increasing.<BR>\n" );
document.write( "I listed the formula.<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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