![]() ![]() where 'a' is the first term and 'r' is the common ratio of the sequence. So a geometric sequence is in form a, ar, ar 2. In other words, in a geometric sequence, every term is multiplied by a constant which results in its next term. This ratio is known as a common ratio of the geometric sequence. Geometric Sequence vs Arithmetic SequenceĪ geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. Sum of Infinite Geometric Sequence Formula Here we shall learn more about each of the above-mentioned geometric sequence formulas along with their proofs and examples. The geometric sequences can be finite or infinite. The sum of an infinite geometric sequence.The recursive formula of a geometric sequence.Here, we learn the following geometric sequence formulas: The common ratio of a geometric sequence can be either negative or positive but it cannot be 0. Here is an example of a geometric sequence is 3, 6, 12, 24, 48. ![]() i.e., To get the next term in the geometric sequence, we have to multiply with a fixed term (known as the common ratio), and to find the preceding term in the sequence, we just have to divide the term by the same common ratio. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term. i.e., when |r| < 1.A geometric sequence is a special type of sequence. The sum of an infinite GP converges when the absolute value of the common ratio of GP is less than 1. When Does the Sum of an Infinite GP Converge? We cannot find the sum of infinite terms of such GP. The sum of finite (n) terms of such GP = a + a + a +. If r = 1, then the GP is of form a, a, a. What is the Geometric Progression Sum Formula with r = 1? In case, |r| ≥ 1 for an infinite GP, then it diverges and hence we cannot find its sum. If GP is infinite, then we can find its sum only when |r| < 1 and we use the formula S ∞ = a/(1-r) in this case. What is the Sum of Geometric Progression Formula for Infinite Terms? If r = 1, then the sum of n terms is S n = n These two formulas would work when r ≠ 1. The sum of n terms in GP with 'a' to be its first term and 'r' to be its common ratio can be found using one of the formulas: The sum of an infinite GP diverges when the absolute value of the common ratio of GP is either equal to 1 or greater than 1. When Does the Sum of an Infinite GP Diverge? ![]() The GP sum formula used to find the sum of n terms in GP is, S n = a(r n - 1) / (r - 1), r ≠ 1 where:
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