Find the 9th term 1, 3/2, 9/4

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

2

3

2

3

gives the next term. In other words,

a

n

=

a

1

⋅

r

n

−

1

a

n

=

a

1

⋅

r

n

-

1

.

Geometric Sequence:

r

=

2

3

r

=

2

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

a

n

=

a

1

r

n

-

1

Substitute in the values of

a

1

=

1

2

a

1

=

1

2

and

r

=

2

3

r

=

2

3

.

a

n

=

(

1

2

)

⋅

(

2

3

)

n

−

1

a

n

=

(

1

2

)

⋅

(

2

3

)

n

-

1

Apply the product rule to

2

3

2

3

.

a

n

=

1

2

⋅

2

n

−

1

3

n

−

1

a

n

=

1

2

⋅

2

n

-

1

3

n

-

1

Multiply

1

2

1

2

and

2

n

−

1

3

n

−

1

2

n

-

1

3

n

-

1

.

a

n

=

2

n

−

1

2

⋅

3

n

−

1

a

n

=

2

n

-

1

2

⋅

3

n

-

1

Cancel the common factor of

2

n

−

1

2

n

-

1

and

2

2

.

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a

n

=

2

n

−

2

3

n

−

1

a

n

=

2

n

-

2

3

n

-

1

Substitute in the value of

n

n

to find the

n

n

th term.

a

5

=

2

(

5

)

−

2

3

(

5

)

−

1

a

5

=

2

(

5

)

-

2

3

(

5

)

-

1

Simplify the numerator.

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a

5

=

8

3

(

5

)

−

1

a

5

=

8

3

(

5

)

-

1

Simplify the denominator.

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a

5

=

8

81

a

5

=

8

81

Step-by-step explanation:

16

step-by-step explanation: