Geometric Series Calculator

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Example

Created on 2024-06-20Asked by Levi Thompson (Solvelet student)

Find the sum of the first 5 terms of the geometric series where the first term

a = 3

and the common ratio

r = 2

Solution

To find the sum of the first 5 terms of the geometric series where the first term

a = 3

and the common ratio

r = 2

: The sum of the first

n

terms of a geometric series is given by:

S_n = a \frac{r^n - 1}{r - 1}

For

n = 5

S_5 = 3 \frac{2^5 - 1}{2 - 1}

= 3 \frac{32 - 1}{1}

= 3 \cdot 31

= 93

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Some of the related questions asked by Evelyn Wilson on Solvelet

1. Calculate the sum of the first 4 terms of the geometric series $5 + 10 + 20 + 40 + \,2. Determine whether the geometric series $3 + 6 + 12 + 24 + \ converges, and if it does, find its sum.,

DefinitionThe sum of the geometric sequence, that is, the terms of the series, is the geometric series It can be finite and it can be infinite all depending on the number of terms being summed. A formula exists for finding the sum of a finite geometric series, but the sum of an infinite geometric series only converges if the common ratio is between -1 and 1. Geometric series are also important in mathematics, economics, and the sciences for analyzing natural processes, financial functions, and signal processing.

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