document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068733>Question 1068733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the sum to 16 terms of the arithmetic  series whose 7th term is 19 and whose 10th  term is 25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683999 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=683999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we are told that we have an arithmetic series, that means there is a common difference between terms. Call it \"d\".\r<BR>\n" );
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document.write( "So, first let's find what that common difference is.\r<BR>\n" );
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document.write( "We are told that the 7th term is 19\r<BR>\n" );
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document.write( "And that the 10th term is 25.\r<BR>\n" );
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document.write( "So we are adding the common difference to get from the 7th to 8th, 8th to 9th, 9th to 10th. Or a total of 3 times.\r<BR>\n" );
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document.write( "So    19 + 3d = 25\r<BR>\n" );
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document.write( "3d = 6\r<BR>\n" );
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document.write( "So d = 2.\r<BR>\n" );
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document.write( "Now let's find the 1st term. We are told that the 7th term is 19, so we add the common difference 6 times from the 1st term.\r<BR>\n" );
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document.write( "or   A_1 + (7-1)*2 =  19\r<BR>\n" );
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document.write( "A_1 + 12 = 19\r<BR>\n" );
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document.write( "A_1 = 7\r<BR>\n" );
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document.write( "So we know the common difference =2, the first term is 7, and we know the number of terms we are adding.\r<BR>\n" );
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document.write( "We still need to know the last term.  So the last term can be found by taking a_10 + (6-1)*2 =  25 + 10 = 35<BR>\n" );
document.write( "The sum is:\r<BR>\n" );
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document.write( "number of terms*(1st term + last term)/2\r<BR>\n" );
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document.write( "16*(7+35)/2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28336%29 ALIGN=MIDDLE  ALT=\"highlight%28336%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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