An arithmetic sequence is a sequence in which the difference between
each consecutive term is constant. An arithmetic sequence can be defined by
an explicit formula in which *a*_{n} = *d* (*n* - 1) + *c*, where *d* is the common
difference between consecutive terms, and *c* = *a*_{1}. An arithmetic sequence can
also be defined recursively by the formulas *a*_{1} = *c*, *a*_{n+1} = *a*_{n} + *d*, in
which *d* is again the common difference between consecutive terms, and *c* is a
constant.

The sum of an infinite arithmetic sequence is either ∞, if *d* > 0, or - ∞, if *d* < 0.

There are two ways to find the sum of a finite arithmetic sequence. To use the
first method, you must know the value of the first term *a*_{1} and the value of
the last term *a*_{n}. Then, the sum of the first *n* terms of the arithmetic
sequence is *S*_{n} = *n*(). To use the second method, you must
know the value of the first term *a*_{1} and the common difference *d*. Then, the
sum of the first *n* terms of an arithmetic sequence is *S*_{n} = *na*_{1} + (*dn* - *d* ).

Previous

Problems Next

Problems