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
2
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
r
=
2
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
=
6
a
1
=
6
and
r
=
2
r
=
2
.
a
n
=
(
6
)
⋅
(
2
)
n
−
1
a
n
=
(
6
)
⋅
(
2
)
n
-
1
Remove parentheses.
a
n
=
6
⋅
2
n
−
1