document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=431863>Question 431863</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.Write in sigma notation:<BR>\n" );
document.write( "0+3+8+15+24+35+48\r<BR>\n" );
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document.write( "2. Find the 10th term of the arithmetic sequence:<BR>\n" );
document.write( "3/4, 13/12,17/12,..\r<BR>\n" );
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document.write( "3. Find the 6th term of the arithmetic sequence:<BR>\n" );
document.write( "a-b, a, a+b,...\r<BR>\n" );
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document.write( "4. The common difference in an arithmetic sequence is 3. The 10th term is 23. Find the first term.\r<BR>\n" );
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document.write( "5. Insert 4 arithmetic means between 5 and 9. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299621 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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/cgi-bin/show-face.mpl?user=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=299621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Looking at the terms of the series, we see that the n-th term is one less than n^2.  For example, the 3rd term = 8 = 3^2 - 1<BR>\n" );
document.write( "So, we can write the series as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28i%5E2-1%2Ci=1%2C7%29 ALIGN=MIDDLE  ALT=\"sum%28i%5E2-1%2Ci=1%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. The arithmetic sequence 3/4,13/12,17/12,... has a common difference of 1/3.<BR>\n" );
document.write( "So we can write: <BR>\n" );
document.write( "a_n = a_1 + (1/3)(n-1)<BR>\n" );
document.write( "Where a_1 is the first term of the sequence<BR>\n" );
document.write( "So the formula for the series becomes:<BR>\n" );
document.write( "a_n = 3/4 + n/3 - 1/3 -> a_n = 5/12 + n/3<BR>\n" );
document.write( "So the 10th term in the sequence is a_10 = 5/12 + 10/3 = 5/12 + 40/12 = 45/12<BR>\n" );
document.write( "3. The common difference is a-(a-b) = b<BR>\n" );
document.write( "So the formula for the series is:<BR>\n" );
document.write( "(a-b) + (n-1)b<BR>\n" );
document.write( "Putting in n=6 gives:<BR>\n" );
document.write( "(a-b) + 5b = a + 4b<BR>\n" );
document.write( "4. An arithmetic series is written a_n = a_1 + (n-1)d<BR>\n" );
document.write( "So we have a_n = a_1 + 3(n-1)<BR>\n" );
document.write( "For n=10, we have<BR>\n" );
document.write( "23 = a_1 + 3(9), or 23 = a_1 + 27<BR>\n" );
document.write( "Therefore a_1 = -4<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );