What is the common ratio for this geometric sequence? 64,16,4,1, ...

Geometric Sequence:

r

=

1

4

r

=

1

4

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

=

64

a

1

=

64

and

r

=

1

4

r

=

1

4

.

a

n

=

(

64

)

⋅

(

1

4

)

n

-

1

a

n

=

(

64

)

⋅

(

1

4

)

n

-

1

Apply the product rule to

1

4

1

4

.

a

n

=

64

⋅

1

n

-

1

4

n

-

1

a

n

=

64

⋅

1

n

-

1

4

n

-

1

One to any power is one.

a

n

=

64

⋅

1

4

n

-

1

a

n

=

64

⋅

1

4

n

-

1

Multiply

64

64

by

1

4

n

-

1

1

4

n

-

1

.

a

n

=

64

(

1

4

n

-

1

)

a

n

=

64

(

1

4

n

-

1

)

Simplify

64

1

4

n

-

1

64

1

4

n

-

1

.

Tap for more steps ...

a

n

=

64

4

n

-

1