Sn = a 1+A2+...+An (1)

S(n- 1) = a 1+a2+..+a(n- 1) (2)

( 1) -(2)

an = Sn-S(n- 1)

Algebra is a branch of mathematics, which studies the general solutions and properties of numbers, quantities, relationships, structures and algebraic equations (groups). Elementary algebra is generally taught in middle schools, introducing the basic ideas of algebra: studying what happens when we add or multiply numbers, understanding the concept of variables and how to establish polynomials and find their roots.

Advanced algebra:

Advanced algebra is a general term for the development of algebra to an advanced stage, including many branches. Higher algebra offered by universities generally includes linear algebra and polynomial algebra.

On the basis of elementary algebra, advanced algebra further expands the research object and introduces many new concepts and quantities which are completely different from usual ones, such as set, vector and vector space. These quantities have operational characteristics similar to numbers, but the research methods and operational methods are more complicated.

A set is the sum of things with certain attributes; Vector is a quantity with both direction and value; Vector space, also called linear space, is a collection of many vectors, which conforms to the rules of some specific operations. The object of operation in vector space is not just a number, but a vector, and its operation properties are also very different.