document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204435>Question 1204435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the 2rd term of a G.p is 180 and the 3rd term is 360, calculate:<BR>\n" );
document.write( "a) the first term <BR>\n" );
document.write( "b) the common ratio<BR>\n" );
document.write( "c) the sum of the first four terms </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840679 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll start with part (b).<BR>\n" );
document.write( "To get the common ratio, we divide any given term over its previous one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r = common ratio<BR>\n" );
document.write( "r = term3/term2<BR>\n" );
document.write( "r = 360/180<BR>\n" );
document.write( "<font color=red>r = 2<BR>\n" );
document.write( "The common ratio is 2.</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We know the 2nd term is 180.<BR>\n" );
document.write( "To get to the third term, we multiply by r = 2.<BR>\n" );
document.write( "To go backwards to the first term, we divide by the common ratio.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "term1 = term2/r<BR>\n" );
document.write( "term1 = 180/2<BR>\n" );
document.write( "<font color=red>term1 = 90</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice that the first equation can be rearranged into r = term2/term1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We know the first three terms are 90, 180, 360.<BR>\n" );
document.write( "The fourth term is 720 since we double 360 to get there.<BR>\n" );
document.write( "Then adding those four terms gets us: 90+180+360+720 = <font color=red>1350</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or we can use this formula<BR>\n" );
document.write( "Sn = sum of the first n terms of a geometric progression (GP)<BR>\n" );
document.write( "Sn = a*(1 - r^n)/(1 - r)<BR>\n" );
document.write( "S4 = 90*(1 - 2^4)/(1 - 2)<BR>\n" );
document.write( "S4 = <font color=red>1350</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Side note: The nth term of this GP is 90*(2)^(n-1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Summary<BR>\n" );
document.write( "(a) first term = <font color=red>90</font><BR>\n" );
document.write( "(b) common ratio = <font color=red>2</font><BR>\n" );
document.write( "(c) sum of first four terms = <font color=red>1350</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );