Which of the following are geometric sequences

B), C) and D)

Step-by-step explanation:

A geometric sequence is the sequence in which the ratio between any two consecutive terms a constant. It is represented by "r".

Common ratio = Second term /First term

The general forma  of a geometric sequence is a. ar. a^2ar^n.

Let's find the common ratio.

A.  4/1 = 4 ; 9/4 = 2.25

The common ratio is not the same through out the sequence. Therefore, it is not a geometric sequence.

B. 5/10 = 1/2 ; 2.5/5 = 1/2 ; 1.25/2.5 = 1/2

The common ratio is the same through the sequence. Therefore it is a geometric sequence.

C. 1, 2, 4, 8,16, 32

Common ratio = 2/1 = 2

4/2 = 2; 8/4 = 2

The common ratio is the same through the sequence. Therefore it is a geometric sequence.

D. 2, -2, 2, -2, 2, -2

The common ratio = -2/2 = -1

-2/2 = -1

So here a = 2 and r = -1

The common ratio is the same through the sequence. Therefore it is a geometric sequence.

Therefore, answer is  B), C) and D)

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