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Geometric Progression (G.P.) is a geometric sequence where each successive term is the result of multiplying a constant number to its preceding term. Learn Nth term, sum of G.P. with examples at BYJU'S.
- 6 min
- Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which...
- The example of GP is: 3, 6, 12, 24, 48, 96,…
- The general form of a Geometric Progression (GP) is given by a, ar, ar 2 , ar 3 , ar 4 ,…,ar n-1 a = First term r = common ratio ar n-1 = nth term
- The common multiple between each successive term and preceding term in a GP is the common ratio. It is a constant value that is multiplied by each...
- If the common ratio between each term of a geometric progression is not equal then it is not a GP.
- If a, ar, ar 2 , ar 3 ,……ar n-1 is the given Geometric Progression, then the formula to find sum of GP is: S n = a + ar + ar 2 + ar 3 +…+ ar n-...
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- Overview
- GP
- Sum of GP
- Common Ratio
This article explains the concept of Geometric Progression (GP) and how to find the sum of a given GP. It also mentions the formula for finding the sum of finite terms in a GP, infinite GP, common ratio in a GP and how to calculate it.
A sequence of terms where each succeeding term is generated by multiplying each preceding term with a constant value, called the common ratio. The sequence is called a geometric progression (GP).
To find the sum of finite terms in a G.P., use formula S n = a + ar + ar^2 + … + ar^n-1 and for infinite G.P., use formula S_∞ = a/(1 - r).
The constant value used to generate each succeeding term in the sequence, also known as the ratio between successive terms.
- 6 min
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The formula for the nth term of a geometric progression whose first term is a and common ratio is r is: a n =ar n-1. The sum of n terms in GP whose first term is a and the common ratio is r can be calculated using the formula: S n = [a (1-r n )] / (1-r). The sum of infinite GP formula is given as: S n = a/ (1-r) where |r|<1.
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