SOLUTION: Identify the 9th term in the geometric sequence. 972, 324, 108, 36,... answers: a) 1/27 b) 4/27 c) 1/81 d) 4/81

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Question 453961: Identify the 9th term in the geometric sequence.
972, 324, 108, 36,...

answers:
a) 1/27
b) 4/27
c) 1/81
d) 4/81
Found 2 solutions by htmentor, solver91311:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
Identify the 9th term in the geometric sequence.
972, 324, 108, 36,...
====================================
First we need to find the common ratio:
r = 324/972 = 1/3
So the n-th term in the sequence is:

So the 9th term is

This simplifies to 4/27
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




So for the 9th term, replace with 9:



The rest is just calculator arithmetic. Hint: Your calculator is going to give you a repeating decimal for an answer. Multiply the calculator result by 3, then do it again, and continue until the calculator gives you a whole number. That is the numerator of your fractional answer. 3 raised to the power of the number of times you multiplied by 3 is the denominator.

John

My calculator said it, I believe it, that settles it
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