# Partial Sum Arithmetic Sequence Calculator

**Created By :** Abhinandan Kumar

**Reviewed By :** Phani Ponnapalli

**Last Updated :** Mar 27, 2023

Free partial sum of arithmetic sequence calculator tool that helps you to display the partial sums of the arithmetic sequence very easily in a small number of seconds. You can use this calculator by giving the input parameters in the given fields and by tapping the calculate button that gives you the desired output.

## Results

### How to Find the Partial Sum of Arithmetic Sequence?

In mathematics, the arithmetic sequence is the set of numbers where the difference between the consecutive terms is different.

Now, if we see the formula for the partial sum of a sequence,

**S _{n} = [(a_{1} + a_{n} )n ] / 2**

where,

S_{n} = partial sum of a sequence.

**a _{n } = a_{1} + (n-1)d**

d = common difference.

a_{1 }= first term of sequence.

Follow the guidelines carefully that are shown below to calculate the partial sum of arithmetic sequence easily.

- Initially, write the values that were given in the problem.
- Then, now you need to find the value of a
_{n}by using the formula, a_{n }= a_{1}+ (n-1)d. - After that, we need to apply the formula to find the partial sum of the sequence, i.e., S
_{n}= [(a_{1}+ a_{n})n ] / 2. - Finally, after substituting the values and simplifying them you will get the output.

**Example:**

**Question: **Find the partial sum of the sequence S_{10}, if a_{1 }= 2, d = 2?

**Solution:**

Given, a_{1 }= 2, d = 2, S_{10} = ?

To find the a_{n }value we need to apply the formula,

**a _{n } = a_{1} + (n-1)d **

a_{10 }= 2 + (9)(2) = 2 + 18 = 20.

Now to find the partial sum of S_{10}

**S _{n} = [(a_{1} + a_{n} )n ] / 2**

As we found the ''a_{n}" value already, substitute that in the formula.

S_{10}= [(a_{1} + a_{n} )n ] / 2

S_{10}= [(2 + 20)10 ] / 2

S_{10}= [(22)10 ] / 2

S_{10}= [(220)] / 2

S_{10}= 110.

Hence, the partial sum of the sequence S_{10} = 110.

For more calculators tools like this, you can go to sequencecalculators.com and make your work easier.

### FAQs on Partial Sum of Sequence Calculator

**1. How do you find the partial sum of the sequence?**

We find the partial sum of a sequence by using the formula, i.e., S_{n} = [(a_{1} + a_{n} )n ] / 2.

**2. What are the steps to use this partial sum of sequence calculator?**

- Firstly, give the input parameters in the fields that are given.
- Next, you need to click on the calculate button.
- Finally, you will see the desired result on the page in seconds.

**3. What is the partial sum of sequence?**

The partial sum of the sequence is nothing but the sum of the part of the sequence.

**4. What do you mean by arithmetic sequence?**

The sequence of numbers that have the difference of any two consecutive terms is constant then is called an arithmetic sequence.