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Solve the Pattern Calculator + Online Solver With Free Steps
The Solve the Pattern Calculator is used to solve for future values of a Sequence; it analyzes and predicts the values which would come next in the sequence. This Calculator is indeed unique, because there is no straightforward method of doing this, and it takes a lot of hits and trials to get the solution to such a problem.
But you need not worry as this Calculator can solve those problems in a blink of an eye. It can also provide a Mathematical Expression describing the sequence itself. And all you need to do is enter the sequence and press the button to get results.
What Is Solve the Pattern Calculator?
The Solve the Pattern Calculator is an online calculator designed to find the solution to your Sequence problems.
This Calculator can not only find out future values of the sequence but also if a viable Mathematical Model exists, it can derive that for the pattern too.
And it does all of it inside your browser with no need for any additional downloads.
How to Use Solve the Pattern Calculator?
To use Solve the Pattern Calculator, you must first enter the sequence comma separated into the input box and then press the button. The step-by-step guide is as follows:
Step 1
It must be noted that the numbers of a pattern have to be comma-separated, otherwise, the calculator would not work. So the first thing to do is to set up the data appropriately.
Step 2
Enter the setup data into the input box labeled “Pattern:” and then press the button “Submit”.
Step 3
Pressing the button will open a new window in front of you with the solution. If you would like to solve more problems, you can simply enter them in the new window and get results.
How Does Solve the Pattern Calculator Work?
A Solve the Pattern Calculator works by taking in a pattern of numbers and then solving a mathematical expression for the said pattern. These patterns are also referred to as Sequences, as one of the very popular sequences is a Fibonacci Sequence.
Now, before we go deeper into the understanding of how a Solve the Pattern Calculator works step-by-step, we first learn about Sequences in more detail.
Sequence
A Sequence is a collection of data points, things if you may but from a mathematical standpoint, these would be Numbers, which are Ordered in some shape or form. A sequence represents some sort of Mathematical Expression at the core of a set of numbers, these could be finite or infinite.
A Sequence can exist in almost infinitely different types of correlations and based on equally many types of mathematical expressions. A generalized definition of a sequence would be:
a1, a2, a3, a4, a5 … an
Where, if 0, 1, 2, 3, 4 … an = n
Solve for a Sequence
To Solve a given pattern or sequence means to find out the values that would Succeed the ones given to us. This is done by using several techniques, which we will go through here.
First, we begin by Analyzing the connection between each entry of the sequence and then trying to find a relationship between them mathematically. It could be generally expressed as:
a1, a2, a3, a4, a5 … an
Where, if 0, 2, 4, 8, 16 … an = 2n
This is how we solve the sequence by finding the mathematical solution to the value an.
Solved Examples
To get a better understanding of the concept, let’s dig deeper using some examples.
Example 1
Consider the pattern:
1, 9, 17, 33, 49, 73
Solve for this sequence and find out the next value in the sequence.
Solution
We begin by first looking at the first three entries from this pattern. You can see that there is a pattern here. The number 9 – 1 = 8, and the number 17 – 9 = 8, so these have a combination based on the value of 8.
Moving forward the pattern changes, as 33 – 17 = 16 which is not equal to 8, but it keeps on for one more value as 49 – 33 = 16.
So we can see that we are adding the multiples of 8 twice in the sequence. And the mathematical expression for this sequence is of the sort:
a0 = 1
a1 = a0 + 8 . 1 = 1 + 8 . 1 = 9
a2 = a1 + 8 . 1 = 9 + 8 . 1 = 17
a3 = a2 + 8 . 2 = 17 + 8 . 2 = 33
a4 = a3 + 8 . 2 = 33 + 8 . 2 = 49
It logically repeats itself as compared to a Mathematical one, but based on the pattern, we can calculate the next value to be 97, added with 24.
Example 2
Consider the given sequence:
0, 1, 1, 3, 5, 11, 21
Calculate the next entry of the sequence and also find the mathematical model of this sequence.
Solution
So we start off the same analyzing strategy for solving this problem, and we can see that the pattern is a bit more complicated to get without the mathematical expression, so let’s try to make sense of it.
a0 = 0
a1 = 2 . a0 + 1 = 2 . 0 + 1 = 1
a2 = 2 . a1 + 1 = 2 . 1 – 1 = 1
a3 = 2 . a2 + 1 = 2 . 1 + 1 = 3
a4 = 2 . a3 + 1 = 2 . 3 – 1 = 5
Hence, we have a recurrent mathematical expression. Therefore, the next value for this sequence would be 43.