Question

Which formula can be used to describe the sequence? -3,3/5,-(3)/(25),(3)/(125),-(3)/(625) A) f(x)=-3((1/5)ˣ⁻¹ B) f(x)=-3(-(1)/(5))ˣ⁻¹ C) f(x)=-(1)/(5) (3)ˣ⁻¹ D) f(x)=-(1)/(5) (-3)ˣ⁻¹

Answer 1

The sequence -3, 3/5, -3/25, 3/125, -3/625 can be described with the formula f(x) = (-1/5)(3^x), which corresponds to option B.

Step-by-step explanation:

The sequence -3, 3/5, -3/25, 3/125, -3/625 can be described with the formula f(x) = (-1/5)(3^x), which corresponds to option B.

Each term in the sequence is obtained by raising -3 to a power of x and dividing it by the corresponding power of 5. The negative exponent in the formula represents the flip to the denominator, indicating division instead of multiplication.

Answer 2

The correct option is D) f(x) = -(1)/(5) * (-3)ˣ⁻¹.

The given sequence is: -3, 3/5, -(3)/(25), (3)/(125), -(3)/(625).

Let's express each term in terms of the first term (-3):

First term: -3

Second term: (-3) / (-5) = 3/5

Third term: (3/5) / (-5) = -(3)/(25)

Fourth term: (-(3)/(25)) / (-5) = (3)/(125)

Fifth term: ((3)/(125)) / (-5) = -(3)/(625)

Now, let's generalize the pattern:

The nth term can be obtained by taking the first term (-3) and multiplying it by
`(-1 / 5)^(n-1)`

So, the correct formula for the sequence is:

`f(x)=-3 *(-1 / 5)^(x-1)`