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F(1)=2/3, f(n) = f(n-1)• 3/2 for n > 2

User ParkCheolu
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1 Answer

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Based on the given information, we can determine the values of f(n) for different values of n.

f(1) = 2/3 (given)

f(2) = f(1) * 3/2 = (2/3) * (3/2) = 1

f(3) = f(2) * 3/2 = 1 * 3/2 = 3/2

f(4) = f(3) * 3/2 = (3/2) * (3/2) = 9/4

f(5) = f(4) * 3/2 = (9/4) * (3/2) = 27/8

In general, we can observe the pattern that f(n) = (2/3) * (3/2)^(n-1).

So, to find f(n) for a specific value of n, substitute it into the formula:

f(n) = (2/3) * (3/2)^(n-1)

For example, if we want to find f(6):

f(6) = (2/3) * (3/2)^(6-1 f(6) = (2/3) * (3/2)^(6-1)
= (2/3) * (3/2)^5
= (2/3) * (243/32)
= 486/96
= 27/16

Therefore, f(6) = 27/16.
User Azzam Alsharafi
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