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Answer:
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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
and
r
=
3
.
a
n
=
(
4
)
⋅
(
3
)
n
−
1
Remove parentheses.
a
n
=
4
⋅
3
n
−
1
Substitute in the value of
n
to find the
n
th term.
a
8
=
4
⋅
3
(
8
)
−
1
Subtract
1
from
8
.
a
8
=
4
⋅
3
7
Raise
3
to the power of
7
.
a
8
=
4
⋅
2187
Multiply
4
by
2187
.
a
8
=
8748