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.

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

2/3x + 7 = 29

step-by-step explanation:

two thirds = 2/3

plus a number = x

at least 29 = 29

there for you should get 2/3x + 7 = 29