Represent the geometric series using the explicit formula.

12, −36, 108, −324, …

f(n) = f(n − 1) ⋅ (−3)
f(n) = f(n − 1) ⋅ (3)
f(n) = 12 ⋅ (−3)(n−1)
f(n) = 12 ⋅ (3)(n−1)

answer:

 f(n)=12(-3)^{(n-1)}

Step-by-step explanation:

The Explicit formula in function notation for a geometric series is:

Where  is the nth term of the sequence,  is the first term in the sequence and  is the common ratio.

Given the following geometric serie:

The common ratio is:

And the first term is:

Therefore, substituting values, we get that the Explicit formula that represents this geometric series is:

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).