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Keith_Richards [23]
3 years ago
15

The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to mode

l the same sequence?
Mathematics
1 answer:
astraxan [27]3 years ago
7 0

Answer:

The explicit formula is Tn = 18[(2/3)^(n-1)]

Where n is the term we are looking for

Step-by-step explanation:

Here, we want to get an explicit formula to model the equation

Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12

F(3) = 2/3 * f(2) = 2/3 * 12 = 8

F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3

F(5) = 2/3 * 16/3 = 32/9

Thus, seeing how the equations are progressing, we can definitely see a pattern.

That is Tn = (2/3)^(n-1)(18)

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