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
1
3
gives the next term. In other words,
a
n
=
a
1
r
n
−
1
.
Geometric Sequence:
r
=
1
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
486
and
r
=
1
3
.
a
n
=
486
(
1
3
)
n
−
1
Apply the product rule to
1
3
.
a
n
=
486
1
n
−
1
3
n
−
1
One to any power is one.
a
n
=
486
1
3
n
−
1
Combine
486
and
1
3
n
−
1
.
a
n
=
486
3
n
−
1
Substitute in the value of
n
to find the
n
th term.
a
5
=
486
3
(
5
)
−
1
Simplify the denominator.
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a
5
=
486
81
Divide
486
by
81
.
a
5
=
6