Answer:
- 12
Step-by-step explanation:
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
−
3
gives the next term. In other words,
a
n
=
a
1
⋅
r
n
−
1
.
Geometric Sequence:
r
=
−
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
4
9
and
r
=
−
3
.
a
n
=
(
4
9
)
⋅
(
−
3
)
n
−
1
Combine
4
9
and
(
−
3
)
n
−
1
.
a
n
=
4
(
−
3
)
n
−
1
9
Substitute in the value of
n
to find the
n
th term.
a
4
=
4
(
−
3
)
(
4
)
−
1
9
Simplify the numerator.
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a
4
=
4
⋅
−
27
9
Simplify the expression.
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a
4
=
−
12
