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 a1, the common difference is d,
and the number of terms is n.
Explicit
Formula: |
an = a1 +
(n – 1)d |
Example 1: |
3, 7, 11, 15, 19 has a1 =
3, d = 4,
and n = 5. The explicit formula is
an = 3 + (n – 1)·4
= 4n – 1 |
Example 2: |
3, –2, –7, –12 has a1 =
3, d = –5,
and n = 4. The explicit formula is
an = 3 +
(n – 1)(–5)
= 8 – 5n
|
See
also
Arithmetic series, geometric sequence
|