Question

Represent the geometric series using the explicit formula. 2, −8, 32, −128, … f(n) = 2 ⋅ (−4)(n−1) f(n) = 2 ⋅ (4)(n−1) f(n) = f(n − 1) ⋅ (−4) f(n) = f(n − 1) ⋅ (4)

Answer 1

Option B

Explanation:

I did the test and I got it right.

Answer 2

Answer:
`f(n)=2(-4)^(n-1)`

Explanation:

The explicit formula for geometric series is given by :_

`f(n)=ar^(n-1)`

, where r= common ratio.

a= first term.

The given geometric series : 2, −8, 32, −128, …

First term = 2

Common ratio =
`(-8)/(2)=-4`

Substitute the value of a and r in (1) , we get

`f(n)=2(-4)^(n-1)`

Hence, the representation of the given geometric series using the explicit formula :
`f(n)=2(-4)^(n-1)`