document.write( "Question 773412: What is the sum of a 6-term geometric series if the first term is 19 and the last term is 319,333? \n" ); document.write( "

Algebra.Com's Answer #471673 by KMST(5328) $\"\"$ $\"About$

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In a geometric sequence the ratio of consecutive terms equals a number $\"r\"$ , called the common ratio.
\n" ); document.write( "The nth term of a geometric sequence is given by
\n" ); document.write( " $\"b%5Bn%5D=b%5B1%5D%2Ar%5E%28n-1%29\"$ where
\n" ); document.write( " $\"b%5B1%5D\"$ is the first term, and
\n" ); document.write( " $\"r\"$ is the common ratio
\n" ); document.write( "The sum of the first n terms is $\"S%5Bn%5D=b%5B1%5D%2A%28r%5En-1%29%2F%28r-1%29\"$
\n" ); document.write( "
\n" ); document.write( "In your case,
\n" ); document.write( " $\"b%5B1%5D=19\"$
\n" ); document.write( " $\"b%5B6%5D=19%2Ar%5E%286-1%29=19%2Ar%5E5=319333\"$
\n" ); document.write( "
\n" ); document.write( " $\"19%2Ar%5E5=319333\"$ --> $\"r%5E5=319333%2F19\"$ --> $\"r%5E5=16087\"$ --> $\"r=root%285%2C16087%29\"$ --> $\"r=7\"$
\n" ); document.write( "
\n" ); document.write( " $\"S%5B6%5D=19%2A%287%5E6-1%29%2F%287-1%29\"$ --> $\"S%5B6%5D=19%2A%28117649-1%29%2F6\"$ --> $\"S%5B6%5D=19%2A117648%2F6\"$ --> $\"highlight%28S%5B6%5D=372552%29\"$ \n" ); document.write( "

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