document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164687>Question 1164687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> NEED HELP<BR>\n" );
document.write( "How do I make a formula for an increasingly decreasing sequence?<BR>\n" );
document.write( "eg: 50,49,47,44,40,35,...<BR>\n" );
document.write( "and how do I find the next three terms of the sequence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789105 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=789105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i found what seems to work.\r<BR>\n" );
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document.write( "formula would be An = A1 - sum of (i - 1) for i = 1 to n.\r<BR>\n" );
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document.write( "formula would work like this:\r<BR>\n" );
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document.write( "when n = 1, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A1 = 50 minus sum of (i - 1) for i = 1 to 1 which becomes:<BR>\n" );
document.write( "A1 = 50 minus 0 which becomes:<BR>\n" );
document.write( "A1 = 50\r<BR>\n" );
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document.write( "when n = 2, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A2 = 50 minus sum of (i - 1) for i = 1 to 2 which becomes:<BR>\n" );
document.write( "A2 = 50 minus 0 minus 1 which becomes:<BR>\n" );
document.write( "A2 = 50 minus 1 which becomes:<BR>\n" );
document.write( "A2 = 49\r<BR>\n" );
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document.write( "when n = 3, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A3 = 50 minus sum of (i - 1) for i = 1 to 3 which becomes:<BR>\n" );
document.write( "A3 = 50 minus 0 minus 1 minus 2 which becomes:<BR>\n" );
document.write( "A3 = 50 minus 3 which becomes:<BR>\n" );
document.write( "A3 = 47\r<BR>\n" );
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document.write( "when n = 4, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A4 = 50 minus sum of (i - 1) for i = 1 to 4 which becomes:<BR>\n" );
document.write( "A4 = 50 minus 0 minus 1 minus 2 minus 3 which becomes:<BR>\n" );
document.write( "A4 = 50 minus 6 which becomes:<BR>\n" );
document.write( "A4 = 44\r<BR>\n" );
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document.write( "when n = 5, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A5 = 50 minus sum of (i - 1) for i = 1 to 5 which becomes:<BR>\n" );
document.write( "A5 = 50 minus sum of 0 minus 1 minus 2 minus 3 minus 4 which becomes:<BR>\n" );
document.write( "A5 = 50 minus 10 which becomes:<BR>\n" );
document.write( "A5 = 40\r<BR>\n" );
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document.write( "when n = 6, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A6 = 50 minus sum of (i = 1) for i = 1 to 6 which becomes:<BR>\n" );
document.write( "A6 = 50 minus 0 minus 1 minus 2 minus 3 minus 4 minus 5 which becomes:<BR>\n" );
document.write( "A6 = 50 minus 15 which becomes:<BR>\n" );
document.write( "A6 = 50 - 15 which becomes:<BR>\n" );
document.write( "A6 = 35\r<BR>\n" );
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document.write( "you can see that this formula gets you the number you are looking for, which are:<BR>\n" );
document.write( "A1 = 50<BR>\n" );
document.write( "A2 = 49<BR>\n" );
document.write( "A3 = 47<BR>\n" );
document.write( "A4 = 44<BR>\n" );
document.write( "A5 = 40<BR>\n" );
document.write( "A6 = 35\r<BR>\n" );
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document.write( "finding the next 3 terms in the sequence is simply applying the formula.\r<BR>\n" );
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document.write( "when n = 7, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A7 = 50 minus sum of (i - 1) for i = 1 to 7 which becomes:<BR>\n" );
document.write( "A7 = 50 minus 0 minus 1 minus 2 minus 3 minus 4 minus 5 minus 6 which becomes:<BR>\n" );
document.write( "A7 = 50 minus 21 which becomes:<BR>\n" );
document.write( "A7 = 29\r<BR>\n" );
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document.write( "when n = 8, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A8 = 50 minus sum of (i - 1) for i = 1 to 8 which becomes:<BR>\n" );
document.write( "A8 = 50 minus 0 minus 1 minus 2 minus 3 minus 4 minus 5 minus 6 minus 7 which becomes:<BR>\n" );
document.write( "A8 = 50 minus 28 which becomes:<BR>\n" );
document.write( "A8 = 22\r<BR>\n" );
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document.write( "when n = 9, An = A1 - sum of (i - 1) for i = 1 to n becomes:<BR>\n" );
document.write( "A9 = 50 minus sum of (i - 1) for i = 1 to 9 which becomes:<BR>\n" );
document.write( "A9 = 50 minus 0 minus 1 minus 2 minus 3 minus 4 minus 5 minus 6 minus 7 minus 8 which becomes:<BR>\n" );
document.write( "A9 = 50 minus 36 which becomes:<BR>\n" );
document.write( "A9 = 14\r<BR>\n" );
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document.write( "to confirm the formula gave you the correct answer, you could do the following.\r<BR>\n" );
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document.write( "you are always subtracting 1 more from the previous number than you subtracted from the number preceding that.\r<BR>\n" );
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document.write( "50 minus 0 = 50 for n = 1<BR>\n" );
document.write( "50 minus 1 = 49 for n = 2<BR>\n" );
document.write( "49 minus 2 = 47 for n = 3<BR>\n" );
document.write( "47 minus 3 = 44 for n = 4<BR>\n" );
document.write( "44 minus 4 = 40 for n = 5<BR>\n" );
document.write( "40 minus 5 = 35 for n = 6<BR>\n" );
document.write( "35 minus 6 = 29 for n = 7<BR>\n" );
document.write( "29 minus 7 = 22 for n = 8<BR>\n" );
document.write( "22 minus 8 = 14 for n = 9\r<BR>\n" );
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document.write( "the formula here appears to be A.n+1 = A.n - (n-1)<BR>\n" );
document.write( "you would start this sequence A1.<BR>\n" );
document.write( "from there the formula would get you.<BR>\n" );
document.write( "A2 = 50 - 1 = 49<BR>\n" );
document.write( "A3 = 49 - 2 = 47<BR>\n" );
document.write( "A4 = 47 - 3 = 44<BR>\n" );
document.write( "A5 = 44 - 4 = 40<BR>\n" );
document.write( "A6 = 40 - 5 = 35<BR>\n" );
document.write( "A7 = 35 - 6 = 29<BR>\n" );
document.write( "A8 = 29 - 7 = 22<BR>\n" );
document.write( "A9 = 22 - 8 = 14\r<BR>\n" );
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document.write( "either way, you can see that A7 will be 29 andA8 will be 22 and A9 will be 14.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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