document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25541>Question 25541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have an assignment due on arithmetic series of numbers. I have been studying my book and can't seem to figure out what I am supposed to do to make or solve the equations. Is there anyway you can help? Thank you in advance.\r<BR>\n" );
document.write( "\n" );
document.write( "Use the arithmetic series of numbers 1,3,5,7,9,...to find the following:\r<BR>\n" );
document.write( "\n" );
document.write( "What is d, the difference between any 2 numbers?\r<BR>\n" );
document.write( "\n" );
document.write( "Using the formula for the nth term of an arithmetic series, what is 101st term?\r<BR>\n" );
document.write( "\n" );
document.write( "Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?\r<BR>\n" );
document.write( "\n" );
document.write( "Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?\r<BR>\n" );
document.write( "\n" );
document.write( "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.)?\r<BR>\n" );
document.write( "\n" );
document.write( "I know it seems like a lot but it really is just one problem broken down into several sections. I have no idea how to so this so I would be VERY thankful for any help you can give me.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13715 by </B><A HREF=/tutors/aboutme.mpl?userid=askmemath><B>askmemath(368)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=askmemath><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=13715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"d\" is the common difference between any 2 consecutive numbers <BR>\n" );
document.write( "In this case the sequence is 1,3,5,7........<BR>\n" );
document.write( "So the difference becomes 3-1= 5-3 = 7-5 = 2\r<BR>\n" );
document.write( "\n" );
document.write( "Now every arithmetic series is represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"a%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a is the first term and d the common difference<BR>\n" );
document.write( "n-1 is the nth term\r<BR>\n" );
document.write( "\n" );
document.write( "For the given series, a = 1 since the series begins with 1 and d = 2<BR>\n" );
document.write( "The 1st term is 1<BR>\n" );
document.write( "2nd term is 3<BR>\n" );
document.write( "So the 101st term becomes 1+(101-1)2  = 1+200 = 201\r<BR>\n" );
document.write( "\n" );
document.write( "Sum to n terms is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2F2%29%2AFirst+Term+%2B+Last+Term ALIGN=MIDDLE  ALT=\"%28n%2F2%29%2AFirst+Term+%2B+Last+Term\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is the number of terms. <BR>\n" );
document.write( "Please solve this on your own as I have already shown you above how to find the last term. Again you can the find the sum to the first 30 terms with the same formula.\r<BR>\n" );
document.write( "\n" );
document.write( "Adding the first two numbers or the first three or so on, you will find that the sum is always an Even Number. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );