Question

Which of the following are geometric sequences

(check all that apply)


A.) 1, 1, 2, 3, 5, 8, 13

B.) 10,5, 2.5, 1.25, 0.625, 0.3125

C.) -9, -3, -1, -1/3, -1/9, -1/27

D.) 5, 10, 15, 20, 25

Answer 1

Answer:

B and C are geometric sequences.

Step-by-step explanation:

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

A is not a geometric sequence because the number 1 is repeated twice in the sequence.

B is a sequence because the sequence is being multiplied by 0.5 each time.

C is a geometric sequence because it is being multiplied by 1/3 each time.

D is not a geometric sequence because it is not being multiplied each time - it is increasing by +5 (arithmetic progression - not geometric).

Hope this helps!

Answer 2

The following are geometric sequences

1. 10,5, 2.5, 1.25, 0.625, 0.3125

2. -9, -3, -1, -1/3, -1/9, -1/27

The correct option is (B) & (C)

What is Geometric sequence?

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

1. A is not a geometric sequence because the '1'  is repeated two times in the sequence.

2. B is a geometric sequence because the sequence is being multiplied by 0.5 each time.

5/10=0.5

2.5/5=0.5

1.25/2.5=0.5

0.625/1.25=0.5

3. C is a geometric sequence because it is being multiplied by 1/3 each time.

-3/-9=1/3

-1/-3=1/3

-1/3/-1= 1/3

-1/9/-1/3= 1/3

4. D is not a geometric sequence because the multiplicative factor is not same.

Hence, 10,5, 2.5, 1.25, 0.625, 0.3125 and -9, -3, -1, -1/3, -1/9, -1/27 is geometric sequence.

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