Given the first term and the common ratio of a geometric sequence find the explicit formula.

31.) a1 = -1, r = -2
(1 is a lowered power to a)

33.) a1 = 4, r = -4
(1 is a lowered power to a)

A geometric sequence is generated by multiplying the first term in the sequence, , several times by a fixed scalar . So

and so on, down to

Using the result above, the sequences you're interested in are

31)

33)

We can rewrite these results to make them slightly cleaner.

2.

according to newton’s cannonball model, what happens if the cannonball's velocity is enough to overpower the pull of earth’s gravitystep-by-step explanation:

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.