document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187276>Question 1187276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A geometric progression has first term a and common ratio r. The sum of the first three terms is 62 and the sum to infinity is 62.5. Find the value of a and the value of r. </SPAN>\n" );
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document.write( "Sum of first three terms: a(1+r+r^2) = 62  [1]<br><BR>\n" );
document.write( "Infinite sum: a(1+r+r^2+...) = 62.5  [2]<br><BR>\n" );
document.write( "Sum of terms starting with the 4th: ar^3(1+r+r^2+...) = 62.5-62 = .5  [3]<br><BR>\n" );
document.write( "Divide [3] by [2]:<br><BR>\n" );
document.write( "r^3 = .5/62.5 = 1/125 = (1/5)^3<br><BR>\n" );
document.write( "r = 1/5<br><BR>\n" );
document.write( "Substitute r=1/5 in [1] to find a:<br><BR>\n" );
document.write( "a(1+1/5+1/25) = 62<BR>\n" );
document.write( "a(1.24) = 62<BR>\n" );
document.write( "a = 62/1.24 = 50<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "a = 50<BR>\n" );
document.write( "r = 1/5<br><BR>\n" );
document.write( " </SPAN>\n" );
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