document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53667>Question 53667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the arithmetic sequence of numbers 1. 3, 5, 7, 9,...to find  the following:<BR>\n" );
document.write( "a) what is d, the differenc between any 2 terms?\r<BR>\n" );
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document.write( "b) Using the formula for the nth term of an arithmetic sequence, what is 101th term?\r<BR>\n" );
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document.write( "c) Using the formula for the sum of an arthmetic series, what is the sum of the first 20 terms? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35909 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=35909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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( "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? <BR>\n" );
document.write( "a(n)=a(1)+(n-1)d<BR>\n" );
document.write( "a(101)=1+(100)2<BR>\n" );
document.write( "a(101)=201<BR>\n" );
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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( "S(n)=(1/2)n(a(1)+a(n))<BR>\n" );
document.write( "S(20)=(1/2)(20)(1+a(20))<BR>\n" );
document.write( "But a(20)=1+19(2)=39<BR>\n" );
document.write( "So S(20)=10(40)=400<BR>\n" );
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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( "Use the formula I just used but let n=30.<BR>\n" );
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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.)? Express your observations as a general formula in \"n.\"<BR>\n" );
document.write( "I gave you the formula in part \"c\".<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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