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2 votes
Enter the explicit rule for the geometric sequence.

9,6,4,83,…

User Allegra
by
4.7k points

2 Answers

3 votes

Final answer:

The explicit rule for the given geometric sequence is an = 9 × (2/3)^(n-1), where an is the nth term, 9 is the first term, and 2/3 is the common ratio.

Step-by-step explanation:

The explicit rule for a geometric sequence can be found by identifying the common ratio between consecutive terms. In this case, since the sequence is 9, 6, 4, ..., we can start by dividing the second term by the first term (6/9 = 2/3) and the third term by the second term (4/6 = 2/3), confirming that the common ratio is 2/3. Therefore, the explicit rule for an nth term, an, of this geometric sequence with the initial term a being 9 (a1 = 9) and common ratio r being 2/3 is given by an = 9 × (2/3)n-1.

User Syed Saad
by
4.6k points
4 votes

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

User Pavel Varchenko
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4.6k points