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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

 


  this page updated 28-jul-14
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes