Without an initial value the best we can do is
XXX
f
(
n
)
=
a
0
−
(
2.5
n
)
where
a
0
is the initial value of the arithmetic sequence.
Explanation:
If the common difference is
(
−
2.5
)
for an arithmetic sequence starting at
a
0
, then
XXX
a
1
=
a
0
−
2.5
XXX
a
2
=
a
1
−
2.5
=
a
0
−
(
2.5
×
2
)
XXX
a
3
=
a
2
−
2.5
=
a
0
−
(
2.5
×
3
)
and in general
XXX
a
n
=
a
n
−
1
−
2.5
=
a
0
−
(
2.5
×
n
Some teachers prefer to start the sequence designated as
a
1
In this case:
XXX
a
n
=
a
1
−
(
2.5
(
n
−
1
)
)
=
a
1
+
2.5
−
2.5
n
