document.write( "Question 980822: In a geometric sequence, the sum of the fourth term to the sixth term is 1\3 the sum of the first three terms. Find the common ratio. \n" ); document.write( "

Algebra.Com's Answer #601919 by KMST(5328) $\"\"$ $\"About$

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In a geometric sequence with first term $\"b%5B0%5D\"$ and common ratio $\"r\"$ ,
\n" ); document.write( " $\"S%5Bn%5D=b%5B0%5D%28%28r%5En-1%29%2F%28r-1%29%29\"$ = sum of the first $\"n\"$ terms.
\n" ); document.write( " $\"S%5B3%5D=b%5B0%5D%28%28r%5E3-1%29%2F%28r-1%29%29\"$ = sum of the first $\"3\"$ terms.
\n" ); document.write( " $\"S%5B6%5D=b%5B0%5D%28%28r%5E6-1%29%2F%28r-1%29%29\"$ = sum of the first $\"n\"$ terms.
\n" ); document.write( "The sum of the fourth term to the sixth term is
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.
\n" ); document.write( "For the geometric sequence described in this problem,
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---> $\"r%5E3=1%2F3\"$ ---> $\"r=root%283%2C1%2F3%29\"$ or $\"r=%281%2F3%29%5E%281%2F3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "NOTE:
\n" ); document.write( "We do not know what the first term is.
\n" ); document.write( "There is an infinite number of different geometric sequences (with different first terms) that fit the description of the problem.
\n" ); document.write( "All of them have the same common ratio. \n" ); document.write( "

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