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

User Auino
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5.0k points

2 Answers

1 vote

Answer:

7.594

Explanation:

User CodingHero
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5.6k points
5 votes

Answer:

2.57

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

User Yugene
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5.1k points