document.write( "Question 1069817: The sum of the first ten terms of a particular arithmetic sequence is four times the sum of the first five terms of the sequence. What is the ratio of the first term to the second term? Express your answer as a common fraction. \n" ); document.write( "

Algebra.Com's Answer #684934 by KMST(5328) $\"\"$ $\"About$

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$\"a%5B1%5D\"$ = the first term,
\n" ); document.write( " $\"d\"$ = the common difference, and
\n" ); document.write( " $\"a%5B2%5D=a%5B1%5D%2Bd\"$ = the second term.
\n" ); document.write( "The sum of the first 5 terms is
\n" ); document.write( " $\"5a%5B1%5D%2B10d\"$ .
\n" ); document.write( "The sum of the first 10 terms is
\n" ); document.write( " $\"10a%5B1%5D%2B45d\"$ .
\n" ); document.write( "The problem says that
\n" ); document.write( " $\"10a%5B1%5D%2B45d=4%285a%5B1%5D%2B10d%29\"$
\n" ); document.write( " $\"10a%5B1%5D%2B45d=20a%5B1%5D%2B40d\"$
\n" ); document.write( " $\"45d-40d=20a%5B1%5D-10a%5B1%5D\"$
\n" ); document.write( " $\"5d=10a%5B1%5D\"$
\n" ); document.write( " $\"d=10a%5B1%5D%2F5\"$
\n" ); document.write( " $\"d%F72a%5B1%5D\"$
\n" ); document.write( "The ratio of the first term to the second term is
\n" ); document.write( " $\"a%5B1%5D%2Fa%5B2%5D\"$ = $\"a%5B1%5D%2F%28a%5B1%5D%2Bd%29\"$ = $\"a%5B1%5D%2F%28a%5B1%5D%2B2a%5B1%5D%29\"$ = $\"a%5B1%5D%2F3a%5B1%5D\"$ = $\"highlight%281%2F3%29\"$ . \n" ); document.write( "

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