document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087609>Question 1087609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assuming one property will be acquired per month. The first month each property is acquired it will house 2 tenants, and the tenants in each property will increase by 2 per month with a maximum of 20 tenants per property. How many tenants will you have after 36 months? What is the formula? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701934 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1 property is acquired each month.\r<BR>\n" );
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document.write( "the first month each property is acquired, it will house 2 tenants.\r<BR>\n" );
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document.write( "the number of tenants in each property will increase by 2 per month with a maximum of 20 tenants per tenants per property.\r<BR>\n" );
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document.write( "how many tenants will you have after 36 months.\r<BR>\n" );
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document.write( "after 36 months, there will be 36 properties.\r<BR>\n" );
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document.write( "each property will have 20 tenants after 10 months.\r<BR>\n" );
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document.write( "that would be the first month the property is purchased plus 9 months after.\r<BR>\n" );
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document.write( "2 + 9 * 2 = 2 + 18 = 20.\r<BR>\n" );
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document.write( "number 36 will have 2<BR>\n" );
document.write( "number 35 will have 4<BR>\n" );
document.write( "number 34 will have 6<BR>\n" );
document.write( "number 33 will have 8<BR>\n" );
document.write( "number 32 will have 10<BR>\n" );
document.write( "number 31 will have 12<BR>\n" );
document.write( "number 30 will have 14<BR>\n" );
document.write( "number 29 will have 16<BR>\n" );
document.write( "number 28 will have 18<BR>\n" );
document.write( "number 27 will have 20\r<BR>\n" );
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document.write( "property numbers 1 through 27 will have 20 each.<BR>\n" );
document.write( "this is the maximum that each property can have.\r<BR>\n" );
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document.write( "there are 9 properties left and those will form an arithmetic progression\r<BR>\n" );
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document.write( "the formula for an arithmetic progeression is An = A1 + (n-1) * d.\r<BR>\n" );
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document.write( "the formula for the sum of an arithmetic progression is Sn = n * (A1 + An) / 2\r<BR>\n" );
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document.write( "A1 is equal to 2.<BR>\n" );
document.write( "d is equal to 2.<BR>\n" );
document.write( "A9 = 2 + 8*2 = 2 + 16 = 18.\r<BR>\n" );
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document.write( "that equates to property number 28.\r<BR>\n" );
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document.write( "note that you are counting down from 36, but your sequence is counting up from 1.\r<BR>\n" );
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document.write( "that means that:\r<BR>\n" );
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document.write( "A1 = property number 36<BR>\n" );
document.write( "A2 = property number 35<BR>\n" );
document.write( "A3 = property number 34<BR>\n" );
document.write( "A4 = property number 33<BR>\n" );
document.write( "A5 = property number 32<BR>\n" );
document.write( "A6 = property number 31<BR>\n" );
document.write( "A7 = property number 30<BR>\n" );
document.write( "A8 = property number 29<BR>\n" );
document.write( "A9 = property number 28\r<BR>\n" );
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document.write( "property number 28 is the 9th property counting down from 36 and including property number 36.\r<BR>\n" );
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document.write( "36 - 29 = 8 + 1 to include 36 = 9\r<BR>\n" );
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document.write( "Sn is equal to 9 * (2 + 18) / 2 = 9 * 20/2 = 9 * 10 = 90\r<BR>\n" );
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document.write( "that equates to the number of tenants in property numbers 28 through 36.\r<BR>\n" );
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document.write( "the total number of tenants is therefore 27 * 20 + 90 = 540 + 90 = 630.\r<BR>\n" );
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document.write( "this can be seen in the following spreadsheet.\r<BR>\n" );
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document.write( "columns are months.<BR>\n" );
document.write( "rows are months.<BR>\n" );
document.write( "data in each cell is the number of tenants in the indicated month.\r<BR>\n" );
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document.write( "months 13 through 25 have been hidden from view so you could see what's happening in the first 12 months and in the last 11 months.\r<BR>\n" );
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document.write( "the bottom row shows the total number of tenants in each month.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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