SOLUTION: Write the equation of this geometric sequence and find the value of the 9th term. 1/3, 1, 3, 9... f(n) = f(9) =

Algebra ->  Formulas -> SOLUTION: Write the equation of this geometric sequence and find the value of the 9th term. 1/3, 1, 3, 9... f(n) = f(9) =       Log On


   

Question 1177666: Write the equation of this geometric sequence and find the value of the 9th term. 1/3, 1, 3, 9... f(n) = f(9) =
Answer by MathLover1(20850) About Me  (Show Source):
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Write the equation of this geometric sequence and find the value of the 9th term.
1%2F3, 1, 3,+9... f%28n%29+=+f%289%29 =

f%5Bn%5D+=+f%5B1%5D%2Ar%5E%28n-1%29 where f%5B1%5D is the first term, f%5Bn%5D is the nth term,+r is the common ratio, and n is the number of terms

given:
f%5B1%5D=1%2F3
f%5B2%5D=1+
find r

r=f%5B2%5D%2Ff%5B1%5D=1%2F%281%2F3%29=3

formula is
f%5Bn%5D+=+%281%2F3%29%2A3%5E%28n-1%29

find f%289%29 => n=9

f%5B9%5D+=+%281%2F3%29%2A3%5E%289-1%29
f%5B9%5D+=+%281%2F3%29%2A3%5E8
f%5B9%5D+=+2187