document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169216>Question 169216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Don't understand sequences, can anyone help?\r<BR>\n" );
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document.write( "Evaluate this sum:<BR>\n" );
document.write( "S= 15 + 9 + 27/5 + 81/25 +....... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124817 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=124817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ahhhhhhh they tried to be tricky on this one....well it simple enough to see we are working with 3's and 5's and that the numerator term say in 27/5 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3 ALIGN=MIDDLE  ALT=\"3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > while the denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E1 ALIGN=MIDDLE  ALT=\"5%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the next term 81/25 is numerator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > while the denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2 ALIGN=MIDDLE  ALT=\"5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, meaning the terms 3 and 5 are increasing by 1 each time.  Its the 1st two terms that are the tricky ones but if you back the exponents up on each of the numerator and denominator making 9= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E1%2F5%5E0 ALIGN=MIDDLE  ALT=\"3%5E1%2F5%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then things begin to make some sense since<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E0=1 ALIGN=MIDDLE  ALT=\"5%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   For 15 you would write this as<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E1%2F5%5E%28-1%29 ALIGN=MIDDLE  ALT=\"3%5E1%2F5%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=15\r<BR>\n" );
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document.write( "so now its easy to see the pattern which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5En%2F5%5E%28n-2%29 ALIGN=MIDDLE  ALT=\"3%5En%2F5%5E%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is natural numbers starting with 1 </SPAN>\n" );
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