document.write( "Question 1205016: The sum of the first three terms of a geometric sequence is 8 and the sum of the first six terms is 12.
\n" ); document.write( "Find the common ratio. \n" ); document.write( "

Algebra.Com's Answer #841621 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "(Informally....)

\n" ); document.write( "The sum of the first 3 terms is 8, and the sum of the first 6 terms is 12.

\n" ); document.write( "That means the sum of terms 4, 5, and 6 is 12-8 = 4.

\n" ); document.write( "The 4th term is equal to the 1st term multiplied by the common ratio 3 times; similarly for the 5th and 2nd, and for the 6th and 3rd. So the sum of terms 4, 5, and 6 is the sum of terms 1, 2, and 3, multiplied by the common ratio 3 times.

\n" ); document.write( "So

\n" ); document.write( " $\"%288%29%28r%5E3%29=4\"$
\n" ); document.write( " $\"r%5E3=0.5\"$
\n" ); document.write( " $\"r=root%283%2C0.5%29\"$

\n" ); document.write( "ANSWER (to a few decimal places): 0.7937

\n" ); document.write( " \n" ); document.write( "

\n" );