document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=850063>Question 850063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 23, 26, 30, 35....is the number of seats in a row of a theatre. 23 being the first row, 26 being the second and so on. give a general solution for the number of seats in the nth row ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511941 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=511941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a quadratic arithmetic series (sometimes known as second difference)\r<BR>\n" );
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document.write( "We notice that the second difference is 1.  (that is the difference is going up by 1).\r<BR>\n" );
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document.write( "In general if we have a second difference a, then the n^2 term is a/2.\r<BR>\n" );
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document.write( "We also know that the first term is 23, so find a_0 which is 21  (23-2).\r<BR>\n" );
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document.write( "so in the form an^2 + bn + c we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29n%5E2+%2B+bn+%2B+22 ALIGN=MIDDLE  ALT=\"%281%2F2%29n%5E2+%2B+bn+%2B+22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We set this equal to one of our rows. We could use 1, but I will use a different one just to prove a point. We know that a_2 = 26. So plug in 2 and see if we get 26.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29+%2A+2%5E2+%2B+2b+%2B+21+=+26 ALIGN=MIDDLE  ALT=\"+%281%2F2%29+%2A+2%5E2+%2B+2b+%2B+21+=+26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%2B+2b+%2B+21+=+26 ALIGN=MIDDLE  ALT=\"+2+%2B+2b+%2B+21+=+26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2b+=+3 ALIGN=MIDDLE  ALT=\"+2b+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+3%2F2+ ALIGN=MIDDLE  ALT=\"+b+=+3%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our form is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29n%5E2+%2B+%283%2F2%29n+%2B21 ALIGN=MIDDLE  ALT=\"%281%2F2%29n%5E2+%2B+%283%2F2%29n+%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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