Gp formula: In a finite GP

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. A Geometric Progression ( GP ) is a sequence of numbers where every term after the first is derived by multiplying the preceding term by a constant factor known as the common ratio. 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 ... GP Sum The sum of a GP is the sum of a few or all terms of a geometric progression. GP sum is calculated by one of the following formulas: Sum of n terms of GP , S n = a (1 - r n) / (1 - r), when r ≠ 1 Sum of infinite terms of GP , S n = a / (1 - r), when |r| < 1 Here, 'a' is the first term and 'r' is the common ratio of GP . A series of numbers obtained by multiplying or dividing each preceding term, such that there is a common ratio between the terms (that is not equal to 0) is the ...