This is an arithmetic sequence since there is a common difference between each term. In this case, adding
3
3
to the previous term in the sequence gives the next term. In other words,
a
n
=
a
1
+
d
(
n
−
1
)
a
n
=
a
1
+
d
(
n
-
1
)
.
Arithmetic Sequence:
d
=
3
d
=
3
This is the formula of an arithmetic sequence.
a
n
=
a
1
+
d
(
n
−
1
)
a
n
=
a
1
+
d
(
n
-
1
)
Substitute in the values of
a
1
=
2
a
1
=
2
and
d
=
3
d
=
3
.
a
n
=
2
+
(
3
)
(
n
−
1
)
a
n
=
2
+
(
3
)
(
n
-
1
)
Simplify each term.
Tap for more steps...
a
n
=
2
+
3
n
−
3
a
n
=
2
+
3
n
-
3
Subtract
3
3
from
2
2
.
a
n
=
3
n
−
1
= 18
