document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241243>Question 241243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) Find the sum of this sequence: 1+3+9+27..3^19<BR>\n" );
document.write( "b) Form the formula by filling in the blank:<BR>\n" );
document.write( "S= a + ar + ar^2 + ar^3 + ... + ar^(n-1)(The series stops at n-1 power because there are n terms, but the first one is not multiplied by r)\r<BR>\n" );
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document.write( "rS=______________?<BR>\n" );
document.write( "rS=___________?(Substritute S-a)<BR>\n" );
document.write( "rS-S=______?<BR>\n" );
document.write( "but rS-S can be factored: rS-S=S(r-1),so<BR>\n" );
document.write( "S=__________?\r<BR>\n" );
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document.write( "I got a), it is 1,743,392,200 But i have no idea how to come up with the formula, even though the book reads the general formula is S=a(r^n-1)/(r-1)<BR>\n" );
document.write( "Please explain. I'm very thankful for your helps!<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 #176696 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=176696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> S= a + ar + ar^2 + ar^3 + ... + ar^(n-1)(The series stops at n-1 power because there are n terms, but the first one is not multiplied by r) <BR>\n" );
document.write( "rS=ar +ar^2 + ar^3 + . . . + ar^n\r<BR>\n" );
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document.write( "Subtract the above equations.  All the middle terms subtract out!\r<BR>\n" );
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document.write( "S-rS = a - ar^n   \r<BR>\n" );
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document.write( "Factor out the S on the left and the a on the right side of the equation:\r<BR>\n" );
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document.write( "S(1-r) = a(1-r^n)\r<BR>\n" );
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document.write( "Divide both sides by (1-r):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%28a%281-r%5En%29%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S=%28a%281-r%5En%29%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This does not agree exactly with your final answer, so multiply both numerator and denominator by -1, and it will give you the final result you are looking for!\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole State College of Florida<BR>\n" );
document.write( "Altamonte Springs Campus  \r<BR>\n" );
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