How To Find the Sum of a Finite Geometric Series

Last Updated on November 11, 2021 by Sagar

Geometric series is the multiplying series, we can find this kind of series sequence common in Mathematics, the “Geometric can be found by finding a series or a list of numbers where each member would exactly found by multiplying the previous term of the number by a ratio which is common in all the number or the term of the sequence.”

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The Geometric Sequence Calculator can be used to find the common ratio or the sequence of increases in the sequence. The geometric series sequences are common in Mathematics and there is always a common ratio or a multiple which can be found to determine the whole series of the sequence. The Geometric series sequences question would become simple to understand if you have perfectly analyzed the precedence sequence of the series. The geometric series calculator is more than useful in determining the sequence pattern in the whole series.

How to represent the Geometric series:

As the geometric series list can be found by determining a common ratio in the list of the Geometric series sequence, so when we are able to find the ratio “r”, then we can simply represent the Geometric series by multiplying this common ratio by each of the preceding numbers, so we can represent the common series sequence as follows:

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  a+ar+ar2+ar3+ar4,…+ar9

We normally call it the finite Geometric series, as the number of the sequence, is not unlimited, so it is a finite series of the sequence and can be easily computed by subjecting to a geometric sequence calculator. On the other hand, the infinite Geometric series are a continual series and it never ends, you can say. The main thing in the finite common series sequence to find the ratio pattern, if we are successfully able to find the ratio “r”, then multiplying each term with this ratio, we can find all the terms, as all the terms can be found by multiplying each term by the exponential values of the of ratio.

 When you multiply the first term with the preceding exponential values of the ratio “r”. Then you can find all the terms in a pattern, this preceding pattern is not difficult to find if you are able to find the “ratio r” of each pattern. Students can use the geometric series sum calculator to find the whole sum and then the ratio of the pattern, you may wonder how to find the sum of a geometric series, for this, we normally use a Sigma notation to describe the whole pattern. If there is an infinite series then we can also use the infinite geometric sequence calculator, keep in mind the infinite Geometric series is a never-ending series pattern. 

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The purpose of the Sigma Notation in Geometric series:

To make the whole geometric series simple, we can use the Sigma Notation, as it can make the whole representation a little simpler and easier to represent and we can understand the whole proceeding sequences by figuring out the Sigma Notation, we can use the Geometric Sequence Calculator to find also the Sigma Notation pattern of the Geometric series.

Now to represent the sum of the whole sequence can be represented by the “n” term of a particular finite geometric series sequence with the given equation:

How To Find the Sum of a Finite Geometric Series

When we are able to understand the Sigma Notation, then it can be easy to determine the whole pattern by putting the values in the preceding sequence to get any term, for example, if we want to find the values of “50th” of a finite Geometric sequence, then we simply have to put the value of the n=49, to get the value of the “50th” term in the proceeding sequence of the Geometric sequence. So by putting the values in the Sigma Notation we can find the values of any proceeding term just by putting the values in the given pattern.

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How can we understand the Sigma Notation Geometric series?

The Sigma Notation is a shorthand representation of the whole Geometric series representation, the SIgma Notation is useful to express the summation or the list of all the consecutive terms in the whole pattern. When we are listing all the preceding terms of the Geometric series, it can be it can time-consuming and sometimes difficult to understand as you need to find a pattern in all the terms, which can be explained in the single Sigma Notation term.

Now you can generate all the range of the values by finding the incremental values in the general pattern of the sequence, we can use the Sigma Notation for the finite and infinite Geometric representation of the pattern as it is a simpler way to represent the whole Geometric pattern irrespective the pattern is finite or the infinite in its nature.

When we rk, then for the lower values the k=0, and it is normally the starting term of the sequence, it is on top of the sequence or the pattern by adding the values of the “n” in the preceding term. We can use the Geometric Sequence Calculator to find the Sigma Notation representation of the whole sequence and to represent the sum of e values of the Geometric series irrespective the series is finite or infinite in its nature, the Sigma Notation is the most simpler way of representing the sequence of the Geometric series pattern.

Now let us consider, we want to represent a Geometric series of up to “10” terms, so we can represent its Sigma Notation representation like that:

How To Find the Sum of a Finite Geometric Series

You have noticed to represent the 10 terms, we are using the final value of the r is “9”, the main reason for this representation is the first term is represented as “ar0″ and the last term is represented as “ar9″, in total it is becoming the ten-term of the Geometric series sequence. So the sigma Notation enabled us to represent the whole Geometric series pattern in a short form, without writing all the terms individually. We can use the Geometric Sequence Calculator by calculator-online.net/geometric-sequence-calculator to find the values of the Geometric series

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