document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203220>Question 1203220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the sequence for -1, 3 , -5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838604 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=838604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "If the terms are odd numbers alternating in sign, then we extend the sequence to get: -1, 3, -5, <font color=red>7, -9, 11, -13, 15, ...</font><BR>\n" );
document.write( "The formula for the nth term would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+%28-1%29%5E%28n%29%2A%282n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+%28-1%29%5E%28n%29%2A%282n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n starts at n = 1<BR>\n" );
document.write( "The 2n-1 portion is always odd when n is an integer.<BR>\n" );
document.write( "The (-1)^n portion alternates the sign from positive to negative, or vice versa. \r<BR>\n" );
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document.write( "Again this assumes the pattern extends like that.\r<BR>\n" );
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document.write( "Another possibility is this sequence: -1, 3, -5, <font color=red>-25, -57, -101, -157, -225, ...</font><BR>\n" );
document.write( "The terms in red are determined from the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+-6n%5E2+%2B+22n+-+17 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+-6n%5E2+%2B+22n+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I used interpolation to find this formula.\r<BR>\n" );
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document.write( "For instance, plug in n = 1 to determine the 1st term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+-6n%5E2+%2B+22n+-+17 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+-6n%5E2+%2B+22n+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+-6%2A1%5E2+%2B+22%2A1+-+17 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+-6%2A1%5E2+%2B+22%2A1+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+-6%2A1+%2B+22%2A1+-+17 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+-6%2A1+%2B+22%2A1+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+-6+%2B+22+-+17 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+-6+%2B+22+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+16+-+17 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+16+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Repeat for n = 2 to arrive at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+3 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and so on.\r<BR>\n" );
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document.write( "Here's another possibility\r<BR>\n" );
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document.write( "The starting sequence is -1, 3, -5<BR>\n" );
document.write( "The gap from -1 to 3 is +4<BR>\n" );
document.write( "The gap from 3 to -5 is -8\r<BR>\n" );
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document.write( "Then the jump from +4 to -8 is \"times -2\"<BR>\n" );
document.write( "If that \"times -2\" pattern holds up, then the next gap could be +16 because -2*(-8) = 16\r<BR>\n" );
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document.write( "So -5 + 16 = 11 could be the next term\r<BR>\n" );
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document.write( "Then the next gap could be -2*16 = -32<BR>\n" );
document.write( "So 11 + (-32) = -21\r<BR>\n" );
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document.write( "Then the next gap could be -2*(-32) = 64<BR>\n" );
document.write( "So -21 + 64 = 43\r<BR>\n" );
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document.write( "-1, 3, -5, <font color=red>11, -21, 43, ...</font>\r<BR>\n" );
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document.write( "As the other tutors have mentioned, questions that ask about the next term in a sequence tend to be too vague. <BR>\n" );
document.write( "If the teacher mentioned something like \"the sequence is arithmetic\" or \"the sequence is geometric\", then it would narrow things down to be able to determine the next term(s).\r<BR>\n" );
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document.write( "In this current state, it is not enough information to simply state \"-1, 3, -5\" and ask for the next term(s).\r<BR>\n" );
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document.write( "Further Reading:<BR>\n" );
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