The number of terms in infinite geometric progression will approach infinity (n = ∞). S n = a 1(1 – r n)/(1 – r), if r 1 Sum of Infinite Terms Multiply both sides of Equation (1) by r (common ratio), we get The sum in geometric progression (known as geometric series) is given by S n = a(1 – r n)/(1 – r), if r 1 Derivation of the Formula Sum of First n Terms of a Geometric Sequence is given by: Where l is the last term What is the sum of the First n Terms of a Geometric Sequence? Given each term of GP as a 1, a 2, a 3, a 4, …, a n, expressing all these terms according to the first term a 1, we getĪ 1 = the first term, a 2 = the second term, and so on Thus to find the nth term of a Geometric Sequence will be :
#Explicit formula for geometric sequence series#
To find the nth term of a Geometric Sequence, we know that the series is in the form of a, ar, ar 2, ar 3, ar 4………. R = successive term/preceding term = ar n-1 / ar n-2 What is the N th Term of a Geometric Sequence? Here, r is the common ratio and a is the scale factor The given sequence can also be written as: Given sequence is a geometric sequence if:Ī 1/a 2 = a 2/a 3 = a 3/a 4 = … = a n-1/a n = r (common ratio) Let the elements of the sequence are denoted by: This ratio is known as the common ratio denoted by ‘r’, where r ≠ 0. Geometric SequenceĪ geometric sequence is the one in which the ratio between two consecutive terms is constant. series with an infinite number of elements is known as infinite series. Infinite Series: When the number of elements in the series is not known, i.e. For example: 1 + 4 + 7 + 10 + … etc.įinite Series: A finite series is one in which the number of elements in the series is known. SeriesĪ series is defined as the sum of the elements of a sequence. Geometric sequence: In contrast, the geometric sequence is the one in which the ratio between two consecutive terms is constant.
This difference is known as common difference.
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