Respuesta :

Answer: Choice A

[tex]a_n = 4\left(\frac{1}{5}\right)^{n-1}[/tex]

This is the same as writing 4(1/5)^(n-1)

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Explanation:

We have a geometric sequence with common ratio r = 1/5 because we multiply each term by this fraction to generate the next term.

eg: 4*(1/5) = 4/5 and (4/5)*(1/5) = 4/25

The starting term is a = 4

The nth term of any geometric sequence is [tex]a_n = a(r)^{n-1}[/tex]

Plugging in those 'a' and r values leads to [tex]a_n = 4\left(\frac{1}{5}\right)^{n-1}[/tex]

Answer:

A.) 4 * (1/5)^(n-1)

Step-by-step explanation:

a1 = 4 * (1/5)^(1-1) = 4* (1/5)^0 = 4*1 = 4

a2 = 4 * (1/5)^(2-1) = 4 * (1/5)^1 = 4 * 1/5 = 4/5

a3 = 4 * (1/5)^(3-1) = 4 * (1/5)^2 = 4 * 1/25 = 4/25

a4 = 4 * (1/5)^(4-1) = 4 * (1/5)^3 = 4 * 1/125 = 4/125

a5 = 4 * (1/5)^(5-1) = 4 * (1/5)^4 = 4 * 1/625 = 4/625

. . .

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