# How do you find the sum of the series #n# from n=1 to 5?

##### 1 Answer

#### Answer:

#### Explanation:

Assuming that you mean that each incremental increase is **arithmetic series** can be calculated. In an arithmetic series, there are a few fundamental variables that must be determined in order to solve the problem (we'll look at these later).

Firstly, let's start with the formula for an arithmetic series:

Alternatively,

Upon simple analysis, you will notice that the second formula uses a new variable,

The term **arithmetic sequence** formula.

The formula used to determine an arithmetic sequence (the arithmetic sequence formula), is given as:

For simplicity, we'll use the first formula. We know that in the sequence:

The first term is

Remember we said that we'd define those variables? Let's do that now. Firstly (in formula 1), we define **common difference**, or the constant difference between each term in the series.

So, we can now calculate the formula. We'll start with

Now, simply solve for

So, we've verified

Now, simply plug

Put simply, in this arithmetic series, the sum of the first

All the best,

Eden