document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204026>Question 1204026</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840011 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=840011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:  <font color=red size=4>248 windows</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "In some countries, the 1st floor is considered to be above the ground floor. <BR>\n" );
document.write( "However, I'll consider the ground floor to be the 1st floor.\r<BR>\n" );
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document.write( "Here's the long way to do it without needing any formulas<BR>\n" );
document.write( "1st floor = 52 windows<BR>\n" );
document.write( "2nd floor = 52-6 = 46 windows<BR>\n" );
document.write( "3rd floor = 46-6 = 40 windows<BR>\n" );
document.write( "4th floor = 40-6 = 34 windows<BR>\n" );
document.write( "5th floor = 34-6 = 28 windows<BR>\n" );
document.write( "6th floor = 28-6 = 22 windows<BR>\n" );
document.write( "7th floor = 22-6 = 16 windows<BR>\n" );
document.write( "8th floor = 16-6 = 10 windows<BR>\n" );
document.write( "In total there are 52+46+40+34+28+22+16+10 = <font color=red>248 windows</font>\r<BR>\n" );
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document.write( "Typing all that into a calculator is fairly tedious. Luckily there's a faster method.<BR>\n" );
document.write( "The sequence 52,46,34,... is arithmetic with<BR>\n" );
document.write( "a1 = 52 = first term<BR>\n" );
document.write( "d = -6 = common difference<BR>\n" );
document.write( "From there we would write:<BR>\n" );
document.write( "Sn = sum of the first n terms<BR>\n" );
document.write( "Sn = (n/2)*(2*a1 + d*(n-1))<BR>\n" );
document.write( "S8 = (8/2)*(2*52 - 6*(8-1))<BR>\n" );
document.write( "S8 = <font color=red>248</font>\r<BR>\n" );
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document.write( "Here's another method.<BR>\n" );
document.write( "The nth term of an arithmetic sequence is: an = a1 + d(n-1)<BR>\n" );
document.write( "Plug in a1 = 52 and d = -6, and simplify, to get an = -6n+58<BR>\n" );
document.write( "Plug in n = 8 to get a8 = 10 to show there are 10 windows on the 8th floor.<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "Sn = sum of the first n terms<BR>\n" );
document.write( "Sn = (n/2)*(first + last)<BR>\n" );
document.write( "Sn = (n/2)*(a1 + an)<BR>\n" );
document.write( "S8 = (8/2)*(a1 + a8)<BR>\n" );
document.write( "S8 = (8/2)*(52 + 10)<BR>\n" );
document.write( "S8 = <font color=red>248</font><BR>\n" );
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