What is the definition of an arithmetic sentence?

Answer 1

An arithmetic sequence is a sequence of numbers such that the difference between successive terms is a constant. This constant is called the common difference and is usually denoted by d.

If the first term is a, then the iterative definition of the sequence is

U(1) = a, and

U(n+1) = U(n) + d for n = 1, 2, 3, ...

Equivalently, the position-to-term rule which defines the sequence is

U(n) = a + (n-1)*d for n = 1, 2, 3, ...