Question

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

Answer 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

Answer 2

r = ¼

Explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

We can get the value for r by dividing aₙ by aₙ₋₁.

a₄/a₃ = ¼

r = ¼