document.write( "Question 700036: in a geometric sequence, the fifth term is 48 and the eighth term is 384. find the first term, the common ratio and the formula for the nth term. \n" ); document.write( "

Algebra.Com's Answer #431810 by KMST(5328) $\"\"$ $\"About$

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$\"a%5B1%5D\"$ =first term
\n" ); document.write( " $\"r\"$ =common ratio
\n" ); document.write( " $\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"$
\n" ); document.write( " $\"a%5B8%5D=a%5B1%5D%2Ar%5E7\"$
\n" ); document.write( " $\"a%5B4%5D=a%5B1%5D%2Ar%5E4\"$
\n" ); document.write( " $\"a%5B8%5D%2Fa%5B4%5D\"$ = $\"a%5B1%5D%2Ar%5E7%2F%28a%5B1%5D%2Ar%5E4%29\"$ = $\"r%5E3\"$
\n" ); document.write( " $\"a%5B8%5D=384\"$ and $\"a%5B4%5D=48\"$
\n" ); document.write( " $\"r%5E3=384%2F48=8=2%5E3\"$
\n" ); document.write( " $\"highlight%28r=2%29\"$
\n" ); document.write( "Substituting $\"r=2\"$ and $\"a%5B4%5D=48\"$ into $\"a%5B4%5D=a%5B1%5D%2Ar%5E4\"$ we get
\n" ); document.write( " $\"48=a%5B1%5D%2A2%5E4\"$ --> $\"48=a%5B1%5D%2A16\"$ --> $\"48%2F16=a%5B1%5D\"$ --> $\"highlight%28a%5B1%5D=3%29\"$
\n" ); document.write( "Substituting $\"r=2\"$ and $\"a%5B1%5D=3\"$ into $\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"$ we get
\n" ); document.write( " $\"highlight%28a%5Bn%5D=3%2A2%5E%28n-1%29%29\"$ \n" ); document.write( "

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