Answer:
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Explanation:
The given figure shows a graph of the values of the terms in a geometric sequence. To find an expression for the nth term of the sequence, we need to identify the pattern in the values.
Looking at the graph, we can observe that the values of the terms are decreasing as n increases. This suggests that the sequence is a decreasing geometric sequence.
In a geometric sequence, each term is found by multiplying the previous term by a constant ratio. Let's denote this ratio as r.
From the graph, we can see that the first term of the sequence (n=0) is 9, and the second term (n=1) is 6. Therefore, we can write the first two terms of the sequence as:
g₀ = 9
g₁ = 6
To find the ratio, we can divide the second term by the first term:
r = g₁ / g₀ = 6 / 9 = 2 / 3
So, the ratio of consecutive terms in the sequence is 2/3.
Now, we can write the expression for the nth term of the geometric sequence as:
gₙ = g₀ * rⁿ
Substituting the values we found earlier:
gₙ = 9 * (2/3)ⁿ
Therefore, the expression for the nth term of the geometric sequence is 9 * (2/3)ⁿ.