document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44629>Question 44629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've got this problem (see below).  I've worked through problems 1b - 1d, but I am stuck with how to answer 1e.  Can someone help?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks A Bunch!\r<BR>\n" );
document.write( "\n" );
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 2 terms? \r<BR>\n" );
document.write( "\n" );
document.write( "Answer: d = 2\r<BR>\n" );
document.write( "\n" );
document.write( "Show work in this space.	\r<BR>\n" );
document.write( "\n" );
document.write( "The difference between any two terms = (n+1 ) th term - (n) th term \r<BR>\n" );
document.write( "\n" );
document.write( "So, the difference d = 3-1 = 5-3 = 7-5 = 2 \r<BR>\n" );
document.write( "\n" );
document.write( "Answer d = 2 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b) 	Using the formula for the nth term of an arithmetic sequence, what is 101st term? <BR>\n" );
document.write( "	<BR>\n" );
document.write( "Answer: nth term = 201\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Show work in this space.	\r<BR>\n" );
document.write( "\n" );
document.write( "Given a = first term = 1 <BR>\n" );
document.write( "n = 101 <BR>\n" );
document.write( "d = 2 <BR>\n" );
document.write( "putting above values in formula 1 <BR>\n" );
document.write( "nth term = 1 + (101-1) * 2 <BR>\n" );
document.write( "= 1 + 200 = 201 <BR>\n" );
document.write( "So, nth term = 201 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c) 	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( "Answer: 400	\r<BR>\n" );
document.write( "\n" );
document.write( "Show work in this space	<BR>\n" );
document.write( "n = 20 <BR>\n" );
document.write( "a = first term = 1 <BR>\n" );
document.write( "So, sum = 20 / 2 (2 * 1 + 19 * 2) <BR>\n" );
document.write( "= 10 * (40) <BR>\n" );
document.write( "sum = 400 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d) 	Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms? =n/2(a +(n-1)d)…………..(1)\r<BR>\n" );
document.write( "\n" );
document.write( "Answer: 900\r<BR>\n" );
document.write( "\n" );
document.write( "Show work in this space	<BR>\n" );
document.write( "given that  n = 30 <BR>\n" );
document.write( "a = first term =1 <BR>\n" );
document.write( "= 30 / 2 (2 * 1 + 29 * 2) <BR>\n" );
document.write( "=15 * (60) <BR>\n" );
document.write( "= 900 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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.\"\r<BR>\n" );
document.write( "\n" );
document.write( "Answer:	<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29503 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=29503\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When \"d\" is a positive number the sum of terms gets<BR>\n" );
document.write( "increasingly greater as you add more terms.\r<BR>\n" );
document.write( "\n" );
document.write( "The sum of \"n\" terms is n times the average of the <BR>\n" );
document.write( "1st and the nth term, i.e. S(n)=(n)[a+(n-1)d]/2\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );