document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979908>Question 979908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first five terms of an AP is 10, the sum of their squares is 380. Find the first term and common difference? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601137 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Let me to decipher the abbreviation &nbsp;<B>AP</B>. &nbsp;It is &nbsp; \"Arithmetic Progression\".\r<BR>\n" );
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document.write( "Let &nbsp;<B>x</B>&nbsp; be the &nbsp;<B>third</B>&nbsp; term of our arithmetic progression and &nbsp;<B>d</B>&nbsp; be its &nbsp;<B>common difference</B>. \r<BR>\n" );
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document.write( "Then the five first terms are\r<BR>\n" );
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document.write( "x - 2d<BR>\n" );
document.write( "x - d<BR>\n" );
document.write( "x<BR>\n" );
document.write( "x + d<BR>\n" );
document.write( "x + 2d.\r<BR>\n" );
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document.write( "The sum of these terms is &nbsp;5x. &nbsp;The sum of their squares is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2 ALIGN=MIDDLE  ALT=\"5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d%5E2 ALIGN=MIDDLE  ALT=\"10d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. &nbsp;It is easy to check.\r<BR>\n" );
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document.write( "Thus we have the system of two &nbsp;(non-linear)&nbsp; equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285x+=+10%2C%0D%0A5x%5E2+%2B+10d%5E2+=+380%29 ALIGN=MIDDLE  ALT=\"system%285x+=+10%2C%0D%0A5x%5E2+%2B+10d%5E2+=+380%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "From the first equation we have &nbsp;x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F5 ALIGN=MIDDLE  ALT=\"10%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.\r<BR>\n" );
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document.write( "Substitute it into the second equation. &nbsp;You will get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A2%5E2 ALIGN=MIDDLE  ALT=\"5%2A2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d%5E2 ALIGN=MIDDLE  ALT=\"10d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=380 ALIGN=MIDDLE  ALT=\"380\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;&nbsp;or&nbsp;&nbsp; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d%5E2 ALIGN=MIDDLE  ALT=\"10d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=380+-+20 ALIGN=MIDDLE  ALT=\"380+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hence, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2 ALIGN=MIDDLE  ALT=\"d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F10 ALIGN=MIDDLE  ALT=\"360%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 36 &nbsp;and&nbsp; d = +/-6.\r<BR>\n" );
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document.write( "Therefore, &nbsp;the members of the progression are \r<BR>\n" );
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document.write( "-10, -4, 2, 8, 14\r<BR>\n" );
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document.write( "- in this order or in the opposite order - it doesn't matter.\r<BR>\n" );
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document.write( "You can check that this progression &nbsp;(or these two progressions)&nbsp; satisfy to the given conditions. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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