document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33525>Question 33525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the first nine terms of an arithmetic progression is 75 and the twenty-fifth is also 75. find the common difference and the sum of the first hundred terms. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19912 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 25th term is a+24d, so a+24d = 75 --eqn1\r<BR>\n" );
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document.write( "Sum of 9 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28n%2F2%29%282a+%2B+%28n-1%29d%29+ ALIGN=MIDDLE  ALT=\"+%28n%2F2%29%282a+%2B+%28n-1%29d%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%289%2F2%29%282a+%2B+%289-1%29d%29+=+75+ ALIGN=MIDDLE  ALT=\"+%289%2F2%29%282a+%2B+%289-1%29d%29+=+75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%282a+%2B+8d%29+=+150+ ALIGN=MIDDLE  ALT=\"+9%282a+%2B+8d%29+=+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18a+%2B+72d+=+150+ ALIGN=MIDDLE  ALT=\"+18a+%2B+72d+=+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Scale eqn1 by 3 to give 3a+72d = 225. So we have \r<BR>\n" );
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document.write( "3a+72d = 225<BR>\n" );
document.write( "18a+72d = 150\r<BR>\n" );
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document.write( "Subtract, to give -15a = 75<BR>\n" );
document.write( "--> a = -5\r<BR>\n" );
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document.write( "So, from a+24d = 75 we get<BR>\n" );
document.write( "-5+24d = 75<BR>\n" );
document.write( "24d = 80<BR>\n" );
document.write( "d = 80/24<BR>\n" );
document.write( "d = 10/3\r<BR>\n" );
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document.write( "This is:<BR>\n" );
document.write( "-5, -5/3, 5/3, 5, 25/3, 35/3, 15, 55/3, 65/3,... which does add up to 75.\r<BR>\n" );
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document.write( "So, Sum of 100 terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28n%2F2%29%282a+%2B+%28n-1%29d%29+ ALIGN=MIDDLE  ALT=\"+%28n%2F2%29%282a+%2B+%28n-1%29d%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28100%2F2%29%282%28-5%29+%2B+%28100-1%29%2810%2F3%29%29+ ALIGN=MIDDLE  ALT=\"+%28100%2F2%29%282%28-5%29+%2B+%28100-1%29%2810%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50%28-10+%2B+%2899%29%2810%2F3%29%29+ ALIGN=MIDDLE  ALT=\"+50%28-10+%2B+%2899%29%2810%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "50(-10 + 330)<BR>\n" );
document.write( "50(320)<BR>\n" );
document.write( "50(320)<BR>\n" );
document.write( "16000\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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