Arithmetic
Sequence
Arithmetic Progression
A sequence such
as 1, 5, 9, 13, 17 or 12, 7, 2, –3, –8, –13, –18
which has a constant difference between terms. The first term
is a_{1}, the common difference is d,
and the number of terms is n.
Explicit
Formula: 
a_{n} = a_{1} +
(n – 1)d 
Example 1: 
3, 7, 11, 15, 19 has a_{1} =
3, d = 4,
and n = 5. The explicit formula is
a_{n} = 3 + (n – 1)·4
= 4n – 1 
Example 2: 
3, –2, –7, –12 has a_{1} =
3, d = –5,
and n = 4. The explicit formula is
a_{n} = 3 +
(n – 1)(–5)
= 8 – 5n

See
also
Arithmetic series, geometric sequence
