document.write( "Question 1043483: pls answer it - the first term of arithmetic mean is 1 and the sum of first 9 terms is equal to369 the first and ninth term of gp coincide with first and ninth term of ap find seventh term of gp \n" ); document.write( "

Algebra.Com's Answer #659140 by KMST(5328) $\"\"$ $\"About$

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WHAT WE KNOW
\n" ); document.write( "There is an ap (arithmetic sequence):
\n" ); document.write( " $\"a%5B1%5D=1\"$ , $\"a%5B2%5D\"$ , $\"a%5B3%5D\"$ , ..... , $\"a%5B9%5D\"$ .
\n" ); document.write( "There is also a gp (geometric sequence):
\n" ); document.write( " $\"b%5B1%5D=a%5B1%5D=1\"$ , $\"b%5B2%5D\"$ , $\"b%5B3%5D\"$ , ..... , $\"b%5B9%5D=b%5B1%5D%2Ar%5E8=1%2Ar%5E8=r%5E8=a%5B9%5D\"$ .
\n" ); document.write( " $\"a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2B%22...%22%2Ba%5B9%5D=9%28a%5B1%5D%2Ba%5B9%5D%29%2F2=369\"$
\n" ); document.write( "We are looking for $\"b%5B7%5D=b%5B1%5D%2Ar%5E6=1%2Ar%5E6=r%5E6\"$
\n" ); document.write( "
\n" ); document.write( "HOW WE FIND THE ANSWER
\n" ); document.write( " $\"9%28a%5B1%5D%2Ba%5B9%5D%29%2F2=369\"$
\n" ); document.write( " $\"%28a%5B1%5D%2Ba%5B9%5D%29%2F2=369%2F9\"$
\n" ); document.write( " $\"%28a%5B1%5D%2Ba%5B9%5D%29%2F2=41\"$
\n" ); document.write( " $\"a%5B1%5D%2Ba%5B9%5D=2%2A41\"$
\n" ); document.write( " $\"a%5B1%5D%2Ba%5B9%5D=82\"$
\n" ); document.write( " $\"1%2Ba%5B9%5D=82\"$
\n" ); document.write( " $\"a%5B9%5D=82-1\"$
\n" ); document.write( " $\"a%5B9%5D=81\"$
\n" ); document.write( "
\n" ); document.write( "So, $\"r%5E8=81\"$ ---> $\"r=root%288%2C81%29=root%288%2C3%5E4%29=sqrt%283%29\"$
\n" ); document.write( "and $\"b%5B7%5D=%28sqrt%283%29%29%5E6\"$
\n" ); document.write( " $\"b%5B7%5D=%283%5E%221+%2F+2%22%29%5E6\"$
\n" ); document.write( " $\"b%5B7%5D=3%5E%28%221+%2F+2%22%2A6%29\"$
\n" ); document.write( " $\"b%5B7%5D=3%5E3\"$
\n" ); document.write( " $\"highlight%28b%5B7%5D=27%29\"$ \n" ); document.write( "

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