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Which sequences are geometric? Select three options.
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4, –4, –12, –20, ...

A, B, D

Step-by-step explanation:

A geometric sequence has terms that are multiplied or divided by the same factor each time, as opposed to an arithmetic, which is addition or subtraction.

So if we divide the terms by each other, we can tell.

-9/-2.7 = -30/-9 = -100/-3, so A is geometric.

2.5/-1 = -6.25/2.5 = 15.625/-6.25, so B is geometric.

9.2/9.1 ≠ 9.3/9.2 ! C is an arithmetic sequence.

.8/8 = .08/.8 = .008/.08, so D is geometric.

-4/4 ≠ -12/-4 ! E is an arithmetic sequence.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}