document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197953>Question 1197953</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your group are running a foundation for street children. Ms. Queen, a friend and rich benefactor, offers two options for her donations:\r<BR>\n" );
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document.write( "Option A: To give $1000 on day 1,  <BR>\n" );
document.write( "$999 on day 2, $998 on day 3, with the process to end after 1000 days. \r<BR>\n" );
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document.write( "Option B: To give $1000 on the first month and increase the<BR>\n" );
document.write( "donation by 12% on the next month. This will continue for 3 years\r<BR>\n" );
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document.write( "You have to tell her which option you will take. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831431 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=831431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Option A has the sequence: 1000, 999, 998, ..., 3, 2, 1\r<BR>\n" );
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document.write( "It is arithmetic with<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;\" > = 1000 = first term<BR>\n" );
document.write( "d = -1 = common difference<BR>\n" );
document.write( "n = 1000 terms\r<BR>\n" );
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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 of an arithmetic sequence\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%282%2Aa%5B1%5D%2Bd%28n-1%29%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+%28n%2F2%29%2A%282%2Aa%5B1%5D%2Bd%28n-1%29%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=S%5B1000%5D+=+%281000%2F2%29%2A%282%2A1000-1%281000-1%29%29 ALIGN=MIDDLE  ALT=\"S%5B1000%5D+=+%281000%2F2%29%2A%282%2A1000-1%281000-1%29%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=S%5B1000%5D+=+500500 ALIGN=MIDDLE  ALT=\"S%5B1000%5D+=+500500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore, adding the terms 1000,999,998,...,3,2,1 will get us the sum 500500<BR>\n" );
document.write( "1000+999+998+...+3+2+1 = 500500\r<BR>\n" );
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document.write( "Option B is a geometric sequence: 1000, 1000*(1.12), 1000*(1.12)^2, ..., 1000*(1.12)^(36-1)\r<BR>\n" );
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document.write( "Note: 3 years = 3*12 = 36 months\r<BR>\n" );
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document.write( "a = 1000 = first term<BR>\n" );
document.write( "r = 1.12 = common ratio, to represent an increase of 12%<BR>\n" );
document.write( "n = 36 = number of terms\r<BR>\n" );
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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 of a geometric sequence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+%28a%2A%281-r%5En%29%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+%28a%2A%281-r%5En%29%29%2F%281-r%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=S%5B36%5D+=+%281000%2A%281-%281.12%29%5E36%29%29%2F%281-1.12%29 ALIGN=MIDDLE  ALT=\"S%5B36%5D+=+%281000%2A%281-%281.12%29%5E36%29%29%2F%281-1.12%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=S%5B36%5D+=+484463.11607167 ALIGN=MIDDLE  ALT=\"S%5B36%5D+=+484463.11607167\"   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=S%5B36%5D+=+484463.12 ALIGN=MIDDLE  ALT=\"S%5B36%5D+=+484463.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you go for option A, then you'll get a total of $500,500.<BR>\n" );
document.write( "If you go for option B, then you'll get a total of $484,463.12\r<BR>\n" );
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document.write( "We see that option A is better by 16036.88 dollars since 500500-484463.12 = 16036.88\r<BR>\n" );
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document.write( "Answer: Option A offers the most money at $500,500.<BR>\n" );
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