Find the 8th term in the following geometric sequence. round your answer to the nearest hundredth. 27/375, 9/75,3/15,1/

  2.57

Step-by-step explanation:

The common ratio of this sequence is ...

  (1/3)/(3/15) = (1/3)/(1/5) = 5/3

Each additional term is 5/3 times the previous one, so the 8th term will be (5/3)^4 times the 4th term (the last one given). It is ...

  (1/3)·(5/3)^4 = 625/243 ≈ 2.57

The generic n-th term (an) is ...

  an = a1·r^(n-1)

where a1 is the first term and r is the common ratio. We can make use of this formula to find the 8th term:

  a8 = (27/375)·(5/3)^7 = (3^3/3^7)·(5^7/(3·5^3)) = 5^4/3^5 = 625/243 ≈ 2.57

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step-by-step explanation: