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Answer:

answerr is This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

1

2

gives the next term. In other words,

a

n

=

a

1

⋅

r

n

−

1

.

Geometric Sequence:

r

=

1

2

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of

a

1

=

200

and

r

=

1

2

.

a

n

=

(

200

)

⋅

(

1

2

)

n

−

1

Simplify the expression.

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a

n

=

200

⋅

1

2

n

−

1

Combine

200

and

1

2

n

−

1

.

a

n

=

200

2

n

−

1

The common ratio is 1/2.

Given that

The sequence 200, 100, 50, 25.

How to find the common ratio?

The common ratio is determined by dividing the second term by the first term.

[tex]\rm Common \ ratio = \dfrac{Second \ Term }{First \ Term}[/tex]

Here, the second term is 100 and the first term is 200.

Then,

The common ratio is;

[tex]\rm Common \ ratio = \dfrac{Second \ Term }{First \ Term}\\\\\rm Common \ ratio = \dfrac{100}{200}[/tex]

[tex]\rm Common \ ratio = \dfrac{1}{2}[/tex]

The common ratio between third term 50 and second term 100 is;

[tex]\rm Common \ ratio = \dfrac{Second \ Term }{First \ Term}\\\\\rm Common \ ratio = \dfrac{50}{100}\\\\\rm Common \ ratio = \dfrac{1}{2}[/tex]

Hence, the common ratio is 1/2.

To know more about the Common ratio click the link given below.

https://brainly.com/question/13162487