This is from PSAT test 2006 Student guide can you please guide me …

27/5,9/5,3/5
38.In the sequence above, each term after the first is equal to 1/3 of the term immediately before it. what is the value of the first term in the sequence that is less than 1/20.

thank you.

 

Expand the sequence a few more steps:

Terms 1-3: \dfrac{27}{5},\dfrac{9}{5},\dfrac{3}{5}

Term 4: \dfrac{3}{5}\times\dfrac{1}{3}=\dfrac{1}{5}

Term 5: \dfrac{1}{5}\times\dfrac{1}{3}=\dfrac{1}{15}

Term 6: \dfrac{1}{15}\times\dfrac{1}{3}=\dfrac{1}{45}

\dfrac{1}{15} is still greater than \dfrac{1}{20}, but \dfrac{1}{45} is less than \dfrac{1}{20}. Therefore, \dfrac{1}{45} is the value you seek.

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