document.write( "Question 1083648: the three consecutive terms in a the G.P are the second third of and sixth term of an A.P find the common ratio? \n" ); document.write( "

Algebra.Com's Answer #697757 by KMST(5328) $\"\"$ $\"About$

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Let's define a couple of variables:
\n" ); document.write( " $\"b\"$ = the first of the three consecutive terms in the G.P.
\n" ); document.write( " $\"r\"$ = the common ratio of the G.P.
\n" ); document.write( "Then, the next two (consecutive) terms in the G.P are
\n" ); document.write( " $\"b%2Ar\"$ = the second of the three consecutive terms in the G.P. ,
\n" ); document.write( "and $\"b%2Ar%5E2\"$ = the third of the three consecutive terms in the G.P.
\n" ); document.write( "The problem probably meant to tell us that
\n" ); document.write( " $\"b\"$ = the second term of the A.P.
\n" ); document.write( " $\"b%2Ar\"$ = the third term of the A.P.
\n" ); document.write( "That makes $\"b%2Ar-b\"$ the common difference of the A.P.
\n" ); document.write( "The problem probably meant to tell us that
\n" ); document.write( " $\"b%2Ar%5E2\"$ = the sixth term of the A.P.
\n" ); document.write( "That would make it $\"4\"$ common differences more than the second term of the A.P.:
\n" ); document.write( " $\"b%2Ar%5E2=b%2B4%2A%28b%2Ar-b%29\"$
\n" ); document.write( "We can simplify and solve for $\"r\"$ the equation above
\n" ); document.write( " $\"b%2Ar%5E2=b%2B4%2A%28b%2Ar-b%29\"$
\n" ); document.write( " $\"b%2Ar%5E2=b%2B4b%2Ar-4b%29\"$
\n" ); document.write( " $\"b%2Ar%5E2-4b%2Ar=-3b\"$
\n" ); document.write( " $\"b%2Ar%5E2-4b%2Ar%2B3b=0\"$
\n" ); document.write( " $\"b%28r%5E2-4r%2B3%29=0\"$
\n" ); document.write( " $\"b%28r-1%29%28r-3%29=0\"$
\n" ); document.write( "We have 3 possible options:
\n" ); document.write( "1) $\"b=0\"$ and $\"r\"$ is undefined,
\n" ); document.write( "probably not the answer expected.
\n" ); document.write( "All the terms of the A.P. and the G.P. would be zero.
\n" ); document.write( "2) $\"r=1\"$ , also probably not the answer expected.
\n" ); document.write( "All the terms of the A.P. and the G.P. would be $\"b\"$ , whatever that value is.
\n" ); document.write( "3) $\"highlight%28r=3%29\"$ is probably the expected answer. \n" ); document.write( "

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