How do Arithmetic Progression and Geometric Progression differ?Įach successive term of a sequence is less than the preceding term by a fixed number, therefore the sequence is an arithmetic progression. In order to find the next term in the geometric progression, we multiply the term with a fixed term known as the common ratio, every time, and if we want to find the preceding term, we divide the term with the same common ratio. This ratio can have both positive and negative values. We must use the given formula and put the first term and constant ratio into the formula in order to calculate the sum of an infinite GP series.Ī geometric progression exists when two successive terms have a common ratio called r. The infinite geometric series with common ratio r such that |r| < 1 can have a sum and it can be calculated by the formula S∞S∞ = a/(1−r), where a is the initial term and r is the common ratio. So the infinite geometric series with common ratio |r| 1 can not have a finite sum.įinding the sum of a geometric progression is not as easy as it sounds. ![]() Which Infinite Geometric Progression has a Sum?Ī geometric progression with an infinite number of terms can have two types of common ratios, the first where |r| 1. The series does not converge, and it has no sum in this case. Let us discuss the infinite series sum formula for both cases. ![]() Depending on the value of r, there arise two cases in infinite series. n is the number of the terms in the seriesĪn infinite geometric series sum formula is used if the number of terms in the geometric sequence is infinite.When the number of terms in a geometric sequence is finite, the sum of the geometric series is calculated as follows: ![]() As we read in the previous section, geometric sequence is of two types, finite and infinite geometric sequences, and the sum of their terms is calculated using different formulas. The geometric progression sum formula is used to calculate the sum of all the terms in a geometric sequence.
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