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What is the explicit rule for the geometric sequence? 25.5, 5.1, 1.02, 0.204, ... an=25.5(15)n an=25.5(15)n−1 an=25.5(15)n+1 an=25.5(15)n+2

User Olegas
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1 Answer

1 vote

Given:

The geometric sequence is:

25.5, 5.1, 1.02, 0.204, ...

To find:

The explicit rule for the given geometric sequence.

Solution:

We have,

25.5, 5.1, 1.02, 0.204, ...

Here, the first term is 25.5 and the common ratio is:


r=(a_2)/(a_1)


r=(5.1)/(25.5)


r=(1)/(5)

The explicit rule for a geometric sequence is:


a_n=ar^(n-1)

Where, a is the first term and r is the common ratio.

Putting
a=25.5,\ r=(1)/(5) in the above formula, we get


a_n=25.5((1)/(5))^(n-1)

Therefore, the correct option is B.

User Harshal Parekh
by
8.0k points
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