document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982910>Question 982910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arithmetic sequence has 1st  term 6 and common difference 624. A geometric sequence has 1st  term 2 and common ratio 3.  Determine an n so the nth  term of the arithmetic sequence is the same as the nth term of the geometric sequence.\r<BR>\n" );
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document.write( "I set this up as:<BR>\n" );
document.write( "a(n) = 6 + (n-1)*624<BR>\n" );
document.write( "a(n) = 2*3^(n-1)\r<BR>\n" );
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document.write( "I set these equal to each other and basically guess and check. When I do this I get a value of 8. \r<BR>\n" );
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document.write( "However, I have seen this done a different way that looks like this:<BR>\n" );
document.write( "a(n) = 6 + 624n <BR>\n" );
document.write( "a(n) = 2*3^n<BR>\n" );
document.write( "3 + 312n = 3^n\r<BR>\n" );
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document.write( "For this I get a value of 7.\r<BR>\n" );
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document.write( "Is the general equation to find a value of n only supposed to be n and not the n-1 that I was using?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603708 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Both ways are correct.  If you start counting at n = 1, then for a(1) to equal 6, you have to have 6 + (1 - 1)*624 and for a(1) to equal 2 for the geometric series, you have to have 2 * 3^(1-1).\r<BR>\n" );
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document.write( "But if you start your count at n = 0, the arithmetic series first term is 6 + 624*0 = 6, and the geometric is 2*3^0 = 2.\r<BR>\n" );
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document.write( "In the first case, 1 to 8 is 8 terms.  In the second case, 0 to 7 is 8 terms.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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