SOLUTION: 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

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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.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D= the first term,
d= the common difference, and
a%5B2%5D=a%5B1%5D%2Bd= the second term.
The sum of the first 5 terms is
5a%5B1%5D%2B10d .
The sum of the first 10 terms is
10a%5B1%5D%2B45d .
The problem says that
10a%5B1%5D%2B45d=4%285a%5B1%5D%2B10d%29
10a%5B1%5D%2B45d=20a%5B1%5D%2B40d
45d-40d=20a%5B1%5D-10a%5B1%5D
5d=10a%5B1%5D
d=10a%5B1%5D%2F5
d%F72a%5B1%5D
The ratio of the first term to the second term is
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 .