An barithmetic sequence/b has a bcommon difference/b ((d)) between consecutive terms.

An barithmetic series/b is the bsum/b of the terms in an arithmetic sequence.

[b]uFormulae[/u]/b

The (n^th) term of an arithmetic sequence is given by:

(u_n=a+(n-1)d)

where (u_n) is the (n^{th}) term,
(a) is the first term, and
(d) is the common difference.

The sum of the first (n) terms in an arithmetic series is given by:

(S_{n=\dfrac{n}{2}(2a+(n-1)d))}

where (S_n) is the sum of the first (n) terms,
(n) is the number of terms being added up,
(a) is the first term, and
(d) is the common difference.

If the last term is known, then this can be written as:

(S_{n=\dfrac{n}{2}(a+l))}

where (S_n) is the sum of the first (n) terms,
(n) is the number of terms being added up,
(a) is the first term, and
(l) is the last term.

[b]uUse of arithmetic sequences and series in modelling[/u]/b

For example, saving schemes where each year a constant amount is paid into an account, e.g. simple interest.

Arithmetic sequences and series:

(u_n=a+(n-1)d)

where (u_n) is the (n^{th}) term, (a) is the first term, and (d) is the common difference.

(S_{n=\dfrac{n}{2}(2a+(n-1)d))}

where (S_n) is the sum of the first (n) terms, (n) is the number of terms being added up, (a) is the first term, and (d) is the common difference.