# 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 **m****athematically**. 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.