document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53538>Question 53538</A>: <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" );
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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" );
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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" );
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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" );
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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" );
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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 #35782 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=35782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) 1,3,5,7,9<BR>\n" );
document.write( "a) d=a(sub n+1)-a(sub n)<BR>\n" );
document.write( "d=3-1=2<BR>\n" );
document.write( "d=5-3=2<BR>\n" );
document.write( "d=7-5=2<BR>\n" );
document.write( "d=9-7=2<BR>\n" );
document.write( "d=2<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "b) a(sub n)= a(sub 1)+(n-1)d<BR>\n" );
document.write( "n=101 <BR>\n" );
document.write( "d=2<BR>\n" );
document.write( "a (sub 1)=1<BR>\n" );
document.write( "a(sub 101)=1+(101-1)2<BR>\n" );
document.write( "a(sub 101)=1+(100)2<BR>\n" );
document.write( "a(sub 101)=1+200<BR>\n" );
document.write( "a(sub 101)=201<BR>\n" );
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document.write( "c) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+n%29=%28n%2F2%29%28a%28sub+1%29%2Ba%28sub+n%29%29 ALIGN=MIDDLE  ALT=\"S%28sub+n%29=%28n%2F2%29%28a%28sub+1%29%2Ba%28sub+n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We need to find a(sub 20) to solve this:<BR>\n" );
document.write( "a(sub 20)=1+(20-1)2<BR>\n" );
document.write( "a(sub 20)=1+(19)2<BR>\n" );
document.write( "a(sub 20)=1+38<BR>\n" );
document.write( "a(sub 20)=39<BR>\n" );
document.write( "n=20<BR>\n" );
document.write( "a(sub 1)=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+20%29=%2820%2F2%29%281%2B39%29 ALIGN=MIDDLE  ALT=\"S%28sub+20%29=%2820%2F2%29%281%2B39%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%28sub+20%29=10%2840%29 ALIGN=MIDDLE  ALT=\"s%28sub+20%29=10%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S(sub 20)=400<BR>\n" );
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document.write( "d)We need to use the formula we used above, but in order to use the formula, we have to find a(sub 30).<BR>\n" );
document.write( "a(sub 30)=1+(30-1)2<BR>\n" );
document.write( "a(sub 30)=1+(29)2<BR>\n" );
document.write( "a(sub 30)=1+58<BR>\n" );
document.write( "a(sub 30)=59<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28sub+30%29=%2830%2F2%29%281%2B59%29 ALIGN=MIDDLE  ALT=\"S%28sub+30%29=%2830%2F2%29%281%2B59%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%28sub+30%29=15%2860%29 ALIGN=MIDDLE  ALT=\"S%28sub+30%29=15%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S(sub 30)=900<BR>\n" );
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document.write( "e)You can use the methods above to find the first 6 S(sub n)'s.<BR>\n" );
document.write( "S(sub 2)=4<BR>\n" );
document.write( "S(sub 3)=9<BR>\n" );
document.write( "S(sub 4)=16<BR>\n" );
document.write( "S(sub 5)=25<BR>\n" );
document.write( "S(sub 6)=36<BR>\n" );
document.write( "Do you see the pattern? (for 2, 2^2=4),(for 3, 3^2=9), ect.<BR>\n" );
document.write( "a(sub n)=1+(n-1)2<BR>\n" );
document.write( "a(sub n)=1+2n-2<BR>\n" );
document.write( "a(sub n)=-1+2n <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28-1%2B2n%29=n%5E2 ALIGN=MIDDLE  ALT=\"sum%28-1%2B2n%29=n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I have a TI-83 and can tell you how to check yourself on a TI-83/84 if you have one.  Let me know if you need the directions for that. </SPAN>\n" );
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