document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151377>Question 1151377</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The third term of a geometric progression is nine times the first term.The sum of the first four terms is K times the first term. Find the values of possible values of K. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773119 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=773119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's say that 'a' is the first term. To get the next term, we multiply by r. We keep this pattern up to generate as many terms as we want.\r<BR>\n" );
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document.write( "first term = a<BR>\n" );
document.write( "second term = (first term)*r = a*r<BR>\n" );
document.write( "third term = (second term)*r = (a*r)*r = ar^2<BR>\n" );
document.write( "fourth term = (third term)*r = (ar^2)*r = ar^3<BR>\n" );
document.write( "and so on...\r<BR>\n" );
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document.write( "Now use the fact that the third term is 9 times the first term<BR>\n" );
document.write( "third term = 9*(first term)<BR>\n" );
document.write( "third term = 9*a<BR>\n" );
document.write( "ar^2 = 9*a<BR>\n" );
document.write( "r^2 = 9 .... divide both sides by 'a'<BR>\n" );
document.write( "r = 3 .... apply square root to both sides\r<BR>\n" );
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document.write( "Use this value of r to compute the first four terms<BR>\n" );
document.write( "first term = a<BR>\n" );
document.write( "second term = a*r = a*3 = 3a<BR>\n" );
document.write( "third term = ar^2 = a(3)^2 = 9a<BR>\n" );
document.write( "fourth term = ar^3 = a(3)^3 = 27a\r<BR>\n" );
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document.write( "Now add them up<BR>\n" );
document.write( "sum of 1st four terms = (1st term)+(2nd term)+(3rd term)+(4th term)<BR>\n" );
document.write( "sum of 1st four terms = (a)+(3a)+(9a)+(27a)<BR>\n" );
document.write( "sum of 1st four terms = 40*a\r<BR>\n" );
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document.write( "We're told that the sum of the first four terms is equal to k times the first term, so set 40*a equal to k*a, and divide both sides by 'a'<BR>\n" );
document.write( "k*a = 40*a<BR>\n" );
document.write( "k = 40\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>k = 40</font><BR>\n" );
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