document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081532>Question 1081532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> express 7+13+19+...+61 using sigma notation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695579 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=695579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is an arithmetic sequence. Take note how we add 6 each time to generate the next term (eg: 7+6 = 13, 13+6 = 19, etc)\r<BR>\n" );
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document.write( "The common difference is therefore d = 6.\r<BR>\n" );
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document.write( "The first term is 7, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+7 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The nth term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5B1%5D%2Bd%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5B1%5D%2Bd%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+7%2B6%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+7%2B6%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+7%2B6n-6 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+7%2B6n-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+6n%2B1 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+6n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the sigma notation summation would be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%286k%2B1%2Ck=1%2C10%29 ALIGN=MIDDLE  ALT=\"sum%286k%2B1%2Ck=1%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how plugging k = 1 leads to<BR>\n" );
document.write( "6*k+1 = 6*1+1 = 7<BR>\n" );
document.write( "which is the first term of the summation string \"7+13+19+...+61\"\r<BR>\n" );
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document.write( "while plugging k = 10 leads to<BR>\n" );
document.write( "6*k+1 = 6*10+1 = 60+1 = 61<BR>\n" );
document.write( "which is the last term of the summation string \"7+13+19+...+61\"\r<BR>\n" );
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document.write( "Note: solving 6k+1 = 61 leads to k = 10\r<BR>\n" );
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document.write( "Final Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%286k%2B1%2Ck=1%2C10%29 ALIGN=MIDDLE  ALT=\"sum%286k%2B1%2Ck=1%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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