SOLUTION: Which term of the geometric sequence 6, 18, 54, … is 118 098?

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Question 1181278: Which term of the geometric sequence 6, 18, 54, … is 118 098?
Answer by MathLover1(20850) About Me  (Show Source):
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Which term of the geometric sequence 6, 18, 54, … is 118 098?
nth term formula is
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
a%5B1%5D=6
a%5B2%5D=18
=>r=18%2F6=3
and your formula is:
a%5Bn%5D=6%2A3%5E%28n-1%29
Which term of the geometric sequence is 118098
118098=6%2A3%5E%28n-1%29....solve for n
118098%2F6=3%5E%28n-1%29
19683=3%5E%28n-1%29........... 19683=3%5E9
3%5E9=3%5E%28n-1%29.........if base same, exponents are same too
9=%28n-1%29
9%2B1=n
n=10
=>118098 is 10th term of the given geometric sequence