What is the defining characteristic of a geometric series

Problem 1EWhat is the defining characteristic of a geometric series Give an example.Answer; Step-1; A sequence ( finite or infinite ) of non zero numbers is called a geometric progression ( abbreviated G.P) iff the ratio of any terms to its preceding term is constant . This non zero constant is usually denoted by ‘r’ and is called common ratio. General term of G.P is = a Thus , if ‘a’ is the first term and ‘r’ is the common ratio , then the G.P is a , ar , a,a………….according as it is finite or infinite.Remarks ; If the last term of a G.P consisting of n terms is denoted by I , then I = a Three numbers a, b , c are in G.P . iff = , i.e . iff = ac Sum of first n terms of a G.P = , r 1 Sum of