Answer:Find the 5th Term 1/2 , 1/3 , 2/9 , 4/27 ,
1
2
,
1
3
,
2
9
,
4
27
,
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
3
gives the next term. In other words,
a
n
=
a
1
⋅
r
n
−
1
.
Geometric Sequence:
r
=
2
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
1
2
and
r
=
2
3
.
a
n
=
(
1
2
)
⋅
(
2
3
)
n
−
1
Apply the product rule to
2
3
.
a
n
=
1
2
⋅
2
n
−
1
3
n
−
1
Multiply
1
2
and
2
n
−
1
3
n
−
1
.
a
n
=
2
n
−
1
2
⋅
3
n
−
1
Cancel the common factor of
2
n
−
1
and
2
.
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a
n
=
2
n
−
2
3
n
−
1
Substitute in the value of
n
to find the
n
th term.
a
5
=
2
(
5
)
−
2
3
(
5
)
−
1
Simplify the numerator.
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a
5
=
8
3
(
5
)
−
1
Simplify the denominator.
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a
5
=
8
81
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