81, 54, 27, 0,...
Find the explicit formula for the arithmetic sequence 81, 54, 27, 0,...
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Step-by-step explanation:
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Algebra Examples
Popular Problems Algebra Identify the Sequence 81 , 54 , 27 , 0
81
,
54
,
27
,
0
This is an arithmetic sequence since there is a common difference between each term. In this case, adding
−
27
to the previous term in the sequence gives the next term. In other words,
a
n
=
a
1
+
d
(
n
−
1
)
.
Arithmetic Sequence:
d
=
−
27
This is the formula of an arithmetic sequence.
a
n
=
a
1
+
d
(
n
−
1
)
Substitute in the values of
a
1
=
81
and
d
=
−
27
.
a
n
=
81
+
(
−
27
)
(
n
−
1
)
Simplify each term.
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a
n
=
81
−
27
n
+
27
Add
81
and
27
.
a
n
=
−
27
n
+
108
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