The sum to n terms of a GP refers to the sum of the first n terms of a GP. In this article, you will learn how to derive the formula to find the sum of n terms of a given GP in different cases along with solved examples.

The formula used for calculating the sum of a geometric series with n terms is Sn = a(1 – r^n)/(1 – r), where r ≠ 1.

Sum of the first n terms: S n = a (r n - 1) / (r - 1) when r ≠ 1 and S n = na when r = 1. Sum of infinite terms: S ∞ = a / (1 - r) when |r| < 1 and the sum is NOT defined when |r| ≥ 1. Let us study each formula in detail in the upcoming sections. To find the n th term of a GP, we require the first term and the common ratio.

2024年5月22日 · This article aims to explain how to calculate the sum of the first n terms of a GP, with the help of various formulas and examples. The formula to calculate the sum of the first n terms of a GP, denoted as a, ar, ar 2, ar 3, …, ar n-1 is: Sn = a [ (rn -1)/ (r-1)] if r ≠ 1. Here: a = First term. r = Common ratio. n = Number of terms.

2025年3月1日 · Tn and Tn-1 are consecutive terms of the GP. Sn is the sum of the first n terms, and >1r>1. Sn is the sum of the first n terms, and <1r<1. l is the last term, and n is the term position from the end. Valid only if 0 < r < 1. Tk = arn-k. Tk is the kth term from the end, and n is the total number of terms.

We will learn how to find the sum of n terms of the Geometric Progression {a, ar, ar 2 2, ar 3 3, ar 4 4, ...........} To prove that the sum of first n terms of the Geometric Progression whose first term ‘a’ and common ratio ‘r’ is given by. S n n = a (rn−1 r−1 r n − 1 r …

What is the Sum of Infinite GP? The sum of infinite GP is nothing but the sum of infinite terms of a GP (Geometric Progression). A GP can be finite or infinite. In the case of an infinite GP, the formula to find the sum of its first 'n' terms is, S n = a (1 - r n) / (1 - r), where 'a' is the first term and 'r' is the common ratio of the GP.

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.

Geometric mean = nth root of the product of ‘n’ terms in the GP. Let ‘a’ be the first term, ‘r’ be the common ratio and ‘n’ be the number of terms. Sum of infinite terms in a GP (r<1) \frac {a} {1-r} 1−ra. Harmonic progression is the series when the reciprocal of the terms are in AP.

Learn important Geometric Progression aptitude formulas with tips curated by our industry professionals in tabular format for easy understanding.