document.write( "Question 1064925: if the sum of first 4 terms of a gp with the first term 5 is 75 then find its common ratio. \n" ); document.write( "

Algebra.Com's Answer #680022 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
Not the only way to solve, but,
\n" ); document.write( " $\"5%2B5r%2B5r%5E2%2B5r%5E3=75\"$
\n" ); document.write( " $\"1%2Br%2Br%5E2%2Br%5E3=15\"$
\n" ); document.write( " $\"r%5E3%2Br%5E2%2Br-14=0\"$
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "Rational roots theorem suggests testing for possible roots -2,-1,-7,1,2,7.\r
\n" ); document.write( "\n" ); document.write( "Best choice to start would be root of 2.\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "2    |    1   1   1   -14\r\n" );
document.write( "     |        2   6   14\r\n" );
document.write( "     ---------------------\r\n" );
document.write( "         1    3   7    0\r\n" );
document.write( "

\n" ); document.write( "The root that works seems to be 2, since remainder in synthetic division was 0. Binomial factor for the cubic equation includes $\"r-2\"$ , so this is the most likely ratio wanted for the question.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"highlight%28r=2%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "check: 5+5*2+5*2*2+5*2*2*2=5+10+20+40=75\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You could also use formula for sum of geometric sequence. \n" ); document.write( "

\n" );