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In the 1st generation, there are 6 rabbits in a forest. Every generation after that, the rabbit population triples. This sequence represents the numbers of rabbits for the first few generations: 6, 18, 54, What is the explicit formula for the number of rabbits in generation n?

In the 1st generation, there are 6 rabbits in a forest. Every generation after that-example-1
User Mansiemans
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1 Answer

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You have the following sequence for the population of the rabbits:

6, 18, 54, ...

The explicit formula for the previous sequence is obtained by considering the values of n (1,2,3,..) for the first terms of the sequence.

You can observe that the explicit formula is:

a(n) = 6·3^(n - 1)

in fact, for n=1,2,3 the result is:

a(1) = 6·3^(1 - 1) = 6·3^0 = 6

a(2) = 6·3^(2 - 1) = 6·3^1 = 18

a(3) = 6·3^(3 - 1) = 6·3^2 = 6·9 = 54

which is consistent with the given sequence 6, 18, 54, ...

User Dezull
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