What is the next term of the geometric sequence?

4/9,-4/3,4, ...

- 12

Step-by-step explanation:

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

-

3

gives the next term. In other words,

a

n

=

a

1

⋅

r

n

-

1

.

Geometric Sequence:

r

=

-

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

-

1

Substitute in the values of

a

1

=

4

9

and

r

=

-

3

.

a

n

=

(

4

9

)

⋅

(

-

3

)

n

-

1

Combine

4

9

and

(

-

3

)

n

-

1

.

a

n

=

4

(

-

3

)

n

-

1

9

Substitute in the value of

n

to find the

n

th term.

a

4

=

4

(

-

3

)

(

4

)

-

1

9

Simplify the numerator.

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a

4

=

4

⋅

-

27

9

Simplify the expression.

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a

4

=

-

12

Answer: 9 is the answer