document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191495>Question 1191495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a given sequence the first term is 3, the last term is 58, and the sum of all the terms is 366. What is the 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 #823265 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=823265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "d = common difference<BR>\n" );
document.write( "n = number of terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = first term = 3<BR>\n" );
document.write( "<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;\" > = nth term or last term = 58<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D ALIGN=MIDDLE  ALT=\"S%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = sum of the first n terms = 366\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%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=366+=+%28n%2F2%29%2A%283%2B58%29 ALIGN=MIDDLE  ALT=\"366+=+%28n%2F2%29%2A%283%2B58%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=366+=+n%2A%281%2F2%29%2A%2861%29 ALIGN=MIDDLE  ALT=\"366+=+n%2A%281%2F2%29%2A%2861%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=366+=+30.5n ALIGN=MIDDLE  ALT=\"366+=+30.5n\"   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=n+=+366%2F%2830.5%29 ALIGN=MIDDLE  ALT=\"n+=+366%2F%2830.5%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=n+=+12 ALIGN=MIDDLE  ALT=\"n+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 12 terms.<BR>\n" );
document.write( "Phrased another way, the 12th term is 58, ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B12%5D+=+58 ALIGN=MIDDLE  ALT=\"a%5B12%5D+=+58\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use this to find the value of d below.<BR>\n" );
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%5B12%5D+=+3%2Bd%2812-1%29 ALIGN=MIDDLE  ALT=\"a%5B12%5D+=+3%2Bd%2812-1%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=58+=+3%2Bd%2812-1%29 ALIGN=MIDDLE  ALT=\"58+=+3%2Bd%2812-1%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=58+=+3%2B11d ALIGN=MIDDLE  ALT=\"58+=+3%2B11d\"   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=11d%2B3+=+58 ALIGN=MIDDLE  ALT=\"11d%2B3+=+58\"   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=11d+=+58-3 ALIGN=MIDDLE  ALT=\"11d+=+58-3\"   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=11d+=+55 ALIGN=MIDDLE  ALT=\"11d+=+55\"   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=d+=+55%2F11 ALIGN=MIDDLE  ALT=\"d+=+55%2F11\"   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=d+=+5 ALIGN=MIDDLE  ALT=\"d+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The common difference is 5. <BR>\n" );
document.write( "This means we add 5 to each term to get the next term.<BR>\n" );
document.write( "The sequence of twelve terms is 3, 8, 13, ..., 53, 58 and these terms add to 366.\r<BR>\n" );
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document.write( "Answer: 5<BR>\n" );
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document.write( " </SPAN>\n" );
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