A sequence is a series of the ratio of two constant terms, and it is represented by a summation index. Sequences are quite common in mathematics and they are quite common. The geometric series is found and determined by multiplying a number by a ratio which is common in all the numbers. The geometric sequence calculator is a simple way to find the sequence of a geometric series.
There is a common factor in all the geometric series , when you are able to identify the common factor then it is possible to identify the whole series. The other name of the geometric series is geometric progression and it is also known as the geometric progression.The next values of the progression can be identified by the multiplying the fixed factor.
What is the geometric series?
The Germatric series is called a geometric progression of the mathematical terms. The items in the terms are multiplied by the non zero elements, sequences are multiplied by a nonzero constant called the general ratio of “r”. The geometric series is progressed by a common ratio, when multiplying a term by a non zero element the next terms appear. You can understand this by a simple example like 2,4,6,8,10…
You can identify the common factor is that all the terms are 2 as when you are multiplying 2 by 2 . you can get the second term and then the next terms by multiplying the 2 by 3. This is 6 then 8 and so on ,the sequences are infinite and we are finishing them by the three dots at the end.
The geometric sequence formula is given by:
a, ar,ar2, ar3, ar4, ar5, ar6….
You can identify all the terms of the geometric sequence by the series sum calculator. You need to know that a, ar,ar2, ar3, ar4, ar5, ar6…. That there is a sequence in the first term to next and then so on. The common factor in all the terms is “a”. The geometric sequence is identified by multiplying all the terms by the common factor “a”, you can see the second term ar is gathered by multiplying the “a” by “r”. The ar2 is determined by the multiplying common factor “a” by the square of the r2 and so on. You can gather all the terms by the geometric sequence calculator.
Example of geometric series:
Determine the Geometric sequence where the first terms a1=2, common ratio =2 and the sum of the first n terms =4.
The geometric series formula for the finding the general terms are given below:
Sn=a1.(1-rn)/1-r
Sn=a1.(1-rn)/1-r
Now by inserting the values in the given formula:
4=2*(1-2n)/1-2
(1-2n)=4/2*/1-2
The geometric series calculator is determining the answer of the given question.
(1-2n)=-2
You can identify all the values by the formula:
(2n)=-2- 1
(2n)=-3
Now take the log of the both sides
log(2n)=log-3
Changing the values of the and applying the rules of log on the terms.
n log(2)=log3
You can get the answer of the geometric sequence is:
n= 1.5849
Conclusion:
The sequence is common in mathematics as we can identify the whole sequence by identifying a common factor. The common ratio calculator can be used to identify the common factor and you can gather a formula for each ratio.