Geometric Series Calculator

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Geometric series is also known as the geometric sequence and the numbers in this series are said to be in Geometric progression. The common ratio between any two successive terms in a geometric series is a constant number. Geometric series calculator is the instant online tool which can calculate the nth term or sum of the numbers in the series.

Example 1: Find the geometric series of first 3 numbers, if the first term of the series is 4 and the common ratio is 1/2.

Here we need to find the geometric series > given first term, a1 = 4

And common ratio, r= 1/2.

‘nth’ term of the geometric sequence > an = a* rn-1

2nd term of the geometric series > a2 = 4 * (1/2)2-1

a2 = 4* (1/2) >  a2 = 2

3rd term of the geometric series > a3 = 4 * (1/2)3-1

a3 = 4 * (1/2)2 > a3 = 4 * ¼ > a3 = 1

Geometric series > 4, 2, 1

Example 2: Find the sum of the above three terms in the geometric series using the Sum formula.

Sum of terms in a Geometric series > Sn = a * (1 – rn)/ (1 – r)

First term, a = 4 and common ratio, r = 1/2 and n = 3 terms.

S3 = 4 * (1 – (1/2)3)/ (1 – 1/2)

S3 = 4 * (1 – 1/8)/ (1/2)

S3 = 4* (7/8)/ (1/2) > S3 = (28/8) * (2/1)

S3 = 7