## An arithmetic series is the sum of a sequence {Un}, n∈Z-+

#### (n is a positive integer)

U(n+1)= Un + k = U(n-1) + 2k = a1 + k×(n)

The sum of the first n terms is then given by Sn = 1/2 * n * (a1+ an)

n times the arithmetic mean of the first and last terms.

## A geometric series is the sum of a sequence {Un} where , n∈Z-*

#### (n is a non negative integer)

U(n+1) = r * Un where r is a constant

The sum of the first n terms is given by Sn = (1-r^(n+1))/(1-r)