document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032514>Question 1032514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hailey is riding a hot-air balloon and accidentally drops her purse over the side. The table shows the height of her purse at different times. When will her purse reach the ground? Show calculations. \r<BR>\n" );
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document.write( "Time (s) -      0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10<BR>\n" );
document.write( "Height (m) - 1000, 995, 980, 955, 920, 875, 820, 755, 680, 595, 500\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647201 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The values for the heights are given recursively as \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D+=+a%5Bn%5D+%2B+d%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D+=+a%5Bn%5D+%2B+d%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bn%5D ALIGN=MIDDLE  ALT=\"d%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an AP with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+-5 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and common difference d = -10. Indeed, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bn%5D+=+-5+%2B+%28n-1%29%28-10%29+=+5+-+10n ALIGN=MIDDLE  ALT=\"d%5Bn%5D+=+-5+%2B+%28n-1%29%28-10%29+=+5+-+10n\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a%5B1%5D+%2B+d%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%5B1%5D+%2B+d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+a%5B2%5D+%2B+d%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+a%5B2%5D+%2B+d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D+=+a%5B3%5D+%2B+d%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B4%5D+=+a%5B3%5D+%2B+d%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( ".........................\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn-1%5D+=+a%5Bn-2%5D+%2B+d%5Bn-2%5D ALIGN=MIDDLE  ALT=\"a%5Bn-1%5D+=+a%5Bn-2%5D+%2B+d%5Bn-2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5Bn-1%5D+%2B+d%5Bn-1%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5Bn-1%5D+%2B+d%5Bn-1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D+=+a%5Bn%5D+%2B+d%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D+=+a%5Bn%5D+%2B+d%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "Adding all the corresponding sides of these equations gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D+=+a%5B1%5D+%2Bd%5B1%5D+%2B+d%5B2%5D ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D+=+a%5B1%5D+%2Bd%5B1%5D+%2B+d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bn%5D ALIGN=MIDDLE  ALT=\"d%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D+=+a%5B1%5D%2B+%28n%2F2%29%28-5+%2B+5-10n%29+=+1000+-+5n%5E2 ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D+=+a%5B1%5D%2B+%28n%2F2%29%28-5+%2B+5-10n%29+=+1000+-+5n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E=0 ALIGN=MIDDLE  ALT=\"n%3E=0\"   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%5Bn%5D+=+1000+-+5%28n-1%29%5E2 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+1000+-+5%28n-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hence let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+1000+-+5%28n-1%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+1000+-+5%28n-1%29%5E2+=+0\"   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+=+1%2B+10sqrt%282%29+=+15.14 ALIGN=MIDDLE  ALT=\"n+=+1%2B+10sqrt%282%29+=+15.14\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds, the time her purse reaches the ground.\r<BR>\n" );
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