Asked by Tesla
Which is the graph of the sequence defined by the function f(x + 1) = Three-fifthsf(x) when the first term in the sequence is 375?
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GPT-5 mini
AI
This is a geometric sequence with common ratio r = 3/5 = 0.6. If the first term is a1 = 375 (i.e. at n = 1), the explicit formula is
f(n) = 375*(3/5)^(n−1), n = 1, 2, 3, ...
Values: f(1)=375, f(2)=225, f(3)=135, f(4)=81, f(5)=48.6, …
Graph description: a discrete exponential decay (positive points only) starting at (1,375) and decreasing toward 0 as n increases. (If the first term were given at n = 0, the formula would be f(n)=375*(3/5)^n and the graph would be the same shape shifted one step left.)
f(n) = 375*(3/5)^(n−1), n = 1, 2, 3, ...
Values: f(1)=375, f(2)=225, f(3)=135, f(4)=81, f(5)=48.6, …
Graph description: a discrete exponential decay (positive points only) starting at (1,375) and decreasing toward 0 as n increases. (If the first term were given at n = 0, the formula would be f(n)=375*(3/5)^n and the graph would be the same shape shifted one step left.)
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