document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173922>Question 1173922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the sum of the first 6 terms of the geometric series with the 3rd term 6 and the common ratio 2/3.<BR>\n" );
document.write( "A) 1330/243<BR>\n" );
document.write( "B) 211/6<BR>\n" );
document.write( "C) 665/18<BR>\n" );
document.write( "D) 665/729 </SPAN>\n" );
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document.write( "For the sum of a geometric series with 6 terms and \"nice\" numbers, finding the numbers and adding them is easier than using the formula for the sum of a finite geometric series.<br><BR>\n" );
document.write( "3rd term 6 and common ratio 2/3 means...<BR>\n" );
document.write( "3rd term 6<BR>\n" );
document.write( "2nd term 6*(3/2) = 9<BR>\n" );
document.write( "1st term 9*(3/2) = 27/2 = 13 1/2<BR>\n" );
document.write( "4th term 6*(2/3) = 4<BR>\n" );
document.write( "5th term 4*(2/3) = 8/3 = 2 2/3<BR>\n" );
document.write( "6th term (8/3(*(2/3) = 16/9 = 1 7/9<br><BR>\n" );
document.write( "With the given answer choices, we can almost choose the right answer without adding the terms.  The denominators of answer choices A and D are powers of 3; those answers are not possible because the 1st term is 27/2.<br><BR>\n" );
document.write( "So the answer is either B or C.  Converting those answer choices to mixed numbers gives<BR>\n" );
document.write( "B: 35 1/6<BR>\n" );
document.write( "C: 36 7/18<br><BR>\n" );
document.write( "Adding the 6 terms....<BR>\n" );
document.write( "13 1/2 + 9 = 22 1/2<BR>\n" );
document.write( "22 1/2 + 6 = 28 1/2<BR>\n" );
document.write( "28 1/2 + 4 = 32 1/2<BR>\n" );
document.write( "32 1/2 + 2 2/3 = 35 1/6<br><BR>\n" );
document.write( "That is already answer B; but it is the sum of just the first 5 terms.  So the answer has to be choice C.  Checking that answer choice....<br><BR>\n" );
document.write( "35 1/6 + 1 7/9 = 35 3/18+1 14/18 = 36 17/18<br><BR>\n" );
document.write( "Yes, answer choice C is the correct sum.<br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );