Learn about the formulas to find the sum of n terms of a geometric progression (GP) for finite and infinite GP. Understand the proofs with solved examples. Understanding this concept ensures you can quickly calculate the total of a geometric series with any number of terms. A sum to n terms of a GP (Geometric Progression) refers to the process of adding up the first n terms of a geometric sequence. The nth for GP can be defined as, an = a1rn-1 In general, GP can be finite and infinite but in the case of infinite GP , the common ratio must be between 0 and 1, or else the values of GP go up to infinity. Sum of GP consists of two cases: Let's denote the Sn are a + ar + ar2 + ..... arn Case 1: If r = 1, the series collapses to a, a, a, a ... In a finite GP , the product of the terms at the same distance from the beginning and the end is the same. It means, a1 × an = a2 × an-1 =...= ak × an-k+1. If we multiply or divide a non-zero quantity by each term of the GP , then the resulting sequence is also in GP with the same common ratio.
