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andre [41]
3 years ago
7

Enter the explicit rule for the geometric sequence. 9,6,4,83,…

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
8 0

Answer:

a_n = 2^(n - 1) 3^(3 - n)


Step-by-step explanation:

9,6,4,8/3,…

a1 = 3^2

a2 = 3 * 2

a3 = 2^2

As we can see, the 3 ^x is decreasing and the 2^ y is increasing

We need to play with the exponent in terms of n

Lets look at the exponent for the base of 2

a1 = 3^2  2^0

a2 = 3^1   2^1

a3 =    3^ 0 2^2

an =   3^      2^(n-1)

I picked n-1  because that is where it starts  0

 n = 1   (1-1) =0

  n=2   (2-1) =1

  n=3  (3-1) =2

Now we need to figure out the exponent for the 3 base

I will pick (3-n)

n =1  (3-1) =2

n =2  (3-2) =1

n=3    (3-3) =0

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