document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169809>Question 169809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> my teacher gave me a homework about sequences.He told us to find the rule between \r<BR>\n" );
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document.write( "1,3,6,10,15,21,can you show the working please and i have to sumit it today.ISBN ACTIVE MATHEMATICS 2 PG 44 EXERCISE 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125198 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=125198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are many ways to find the sequence, but here's a little trick\r<BR>\n" );
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document.write( "1,3,6,10,15,21 ... Start with the given sequence\r<BR>\n" );
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document.write( "2,6,12,20,30,42 ... Multiply EVERY term by 2\r<BR>\n" );
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document.write( "So we now have the sequence\r<BR>\n" );
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document.write( "2,6,12,20,30,42\r<BR>\n" );
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document.write( "So if we start at n=1, then when n=1, the term <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;\" > is 2. If n=2, the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 6. If n=3, the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 12, etc...\r<BR>\n" );
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document.write( "So we have this set up\r<BR>\n" );
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document.write( "<tr><TD ><b>n</b></TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD></tr>\r\n" );
document.write( "<tr><TD ><b>Term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ></b></TD><TD >2</TD><TD >6</TD><TD >12</TD><TD >20</TD><TD >30</TD><TD >42</TD></tr>\r\n" );
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document.write( "Notice how the term 2 is equal to 1*2 (where 1 is the value of n and 2 is the next number). Also, notice how 6=2*3 (where 2 is the value of n and 3 is the next number). Furthermore, take note that 12=3*4 (where 3 is the value of n and 4 is the next number) etc....\r<BR>\n" );
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document.write( "So ANY term in this sequence can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For instance, let's say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=4 ALIGN=MIDDLE  ALT=\"n=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This would mean that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29=4%284%2B1%29=4%285%29=20 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29=4%284%2B1%29=4%285%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=3 ALIGN=MIDDLE  ALT=\"n=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the term is 12\r<BR>\n" );
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document.write( "Before we can wrap this up, we need to divide the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Why? Because we multiplied every term of the original sequence by 2. So we need to divide by 2 to get back to the original expression. \r<BR>\n" );
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document.write( "So the formula for the sequence 1,3,6,10,15,21 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=%28n%28n%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=%28n%28n%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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