What is the iterative rule for the following sequence?
4, 4/5, 4/25, 4/125, ...

A.) an=4•(1/5)^n-1
B.) an=4•(1/5)^n
C.) an=1/5•4^n-1
D.) an=1/5•4^n

Answers

Answer 1

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

. . .

Answer 2

The required iterative rule for the following sequence is [tex]a_n=4*(1/5)^{n-1}[/tex]. Option A is correct.

Given sequence,
4, 4/5, 4/25, 4/125, ...

What is geometric progression?

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
The given sequence is 4, 4/5, 4/25, 4/125, ...

Common ratio among the proceeding terms,
r = 4/5/4
r = 1/5
The required general term can be described as [tex]a_n=4*(1/5)^{n-1}[/tex].

Thus, the required iterative rule for the following sequence is [tex]a_n=4*(1/5)^{n-1}[/tex]. Option A is correct.

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Answers

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Have a blessed day <333

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