# Finding a formula for a difficult sequence

• torquerotates
In summary, a formula for a difficult sequence is a mathematical equation or rule used to generate terms and predict future terms without manual calculations. There is no set process for finding a formula, but methods such as identifying patterns, using algebra, or known formulas can be helpful. Not all difficult sequences have a formula, but finding one can provide a deeper understanding and aid in calculations for various applications. There are tools and resources available, but manual methods may still be necessary.

## Homework Statement

I'm trying to find a formula for 1, 3, 6, 10 ... for n=2,3,4,...

## The Attempt at a Solution

Well I know that the difference between each number is increasing by 1. For example, the difference between 1 and 3 is 2, between 3 and 6 is 3, between 6 and 10 is 4 and so on. But, I just don't see a formula.

Hi! $$a_n = \sum_{ k = 1 }^n k = \frac{ n ( n + 1 ) }{ 2 }$$

For some reason, I can't read that.

## 1. What is a formula for a difficult sequence?

A formula for a difficult sequence is a mathematical equation or rule that can be used to generate the terms in a sequence. It can help to predict the next terms in the sequence without having to manually calculate them.

## 2. How do you find a formula for a difficult sequence?

There is no set process for finding a formula for a difficult sequence, as it can vary depending on the sequence. However, some common methods include looking for patterns in the sequence, using algebraic manipulations, or using known formulas for similar sequences.

## 3. Can a formula be found for any difficult sequence?

It depends on the sequence. Some sequences may have a pattern or rule that can be expressed in a formula, while others may not. In some cases, it may be impossible to find a formula for a sequence.

## 4. Why is it important to find a formula for a difficult sequence?

Finding a formula for a difficult sequence can provide a deeper understanding of the sequence and its underlying patterns. It can also make it easier to calculate future terms in the sequence, which can be useful in various applications such as in mathematics, physics, and computer science.

## 5. Are there any tools or resources that can help in finding a formula for a difficult sequence?

Yes, there are various tools and resources available such as online sequence solvers, textbooks on sequences and series, and mathematical software programs. However, it is important to note that these tools may not always be able to find a formula for a difficult sequence, and manual methods may be required.