document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73025>Question 73025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1)use the arithmatic 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 terms?<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "show work:\r<BR>\n" );
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document.write( "b)using the formula for the nth term of an arithmetic sequence, what is the 101st term?<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "show work:\r<BR>\n" );
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document.write( "c) using the formula for the sum of an arithmeitc sequence, what is the sum of the first 20 terms?<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "show work:\r<BR>\n" );
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document.write( "d)using the formula for the sum of an arithmetic sequence, wht is the sum of the first 30 terms?<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "show work:\r<BR>\n" );
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document.write( "e)what observaton can you make about these sums of this sequence? express your observations as a general formula in \"n\". </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52279 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=52279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1)use the arithmatic 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 terms?<BR>\n" );
document.write( "answer: 3-1=2 or 5-3=2: the common difference is \"2\"<BR>\n" );
document.write( "show work: <BR>\n" );
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document.write( "b)using the formula for the nth term of an arithmetic sequence, what is the 101st term?<BR>\n" );
document.write( "answer: a(101)= a(1)+(100)(2) = 1+200 = 201<BR>\n" );
document.write( "show work: a(n)=a(1)+(n-1)d<BR>\n" );
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document.write( "c) using the formula for the sum of an arithmeitc sequence, what is the sum of the first 20 terms?<BR>\n" );
document.write( "answer<BR>\n" );
document.write( "S(n)=(n/2)(a(1)+a(n))<BR>\n" );
document.write( "S(20) = 10(1+a(20))<BR>\n" );
document.write( "But a(20)=1+19*2=39<BR>\n" );
document.write( "So, S(20)=10(1+39)=400<BR>\n" );
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document.write( "d)using the formula for the sum of an arithmetic sequence, wht is the sum of the first 30 terms?<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "S(30)=15(1+a(30))<BR>\n" );
document.write( "But a(30)=1+29*2=59<BR>\n" );
document.write( "So S(30)=15*60=900<BR>\n" );
document.write( "show work: <BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "e)what observaton can you make about these sums of this sequence? express your observations as a general formula in \"n\".<BR>\n" );
document.write( "As n gets larger  S(n) gets larger.<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" );
document.write( "</TD></TR></TABLE>\n" );