# Sum of Linear Number Sequence Calculator - Handy & Free Online Tool

**Created By :** Abhinandan Kumar

**Reviewed By :** Rajashekhar Valipishetty

**Last Updated :** Mar 23, 2023

SequenceCalculators' Sum of Linear Number Sequence Calculator - Handy & Free Online Tool is an online tool that assists everyone to add up numbers in a linear sequence. Simply enter the input numbers in the calculator and click on the calculate button to obtain the output with steps in just a few seconds.

### What is meant by Sum of Linear Number Sequence?

A set of values where every consecutive one differs by the same amount from the previous one is referred to as finding the Sum of Linear Number Sequence.

For Example, if we consider the sequence of 5 numbers as 10, 15, 20, 25, 30 and with the initial value as 10, final value as 30, difference between the successive figures as 5. Then, the sum of all of these numbers is 45.

### How to Calculate the Summation of Linear Number Sequence?

To find the Sum of Linear Number Sequence, we have to apply the sum of AP formula. Before that, we need to find the required terms like initial value, difference, periods, and final value. If we miss any of the term in the given sequence, then finding the Sum of Linear Number Sequence can be tricky & time-consuming.

The formulas that we use to find any of the missed terms are listed below and they are obtained from the sum of the arithmetic sequence formula:

1. Want to find initial value using difference, periods, and final value? Then the formula is given as Initial Value = Final Value - (Periods-1) * Difference

2. For finding difference between two successive values using final value, initial values, and periods, the formula is given as Difference = (Final Value - Initial Value)/ (Periods-1))

3. To calculate the periods using the final value, initial values and difference, the formulas is given as Periods = ((Final Value - Initial Value)/Difference)+1

4. For solving the final value using the initial value, periods, and difference, the formula is given by Final Value = Initial Value + (Periods-1)*Difference

Finally, after calculating all the required terms of the sequence by using the above formulas, we can easily find the sum of linear number sequence with the formula called Sn = (n/2) * (a+l).

Where,

- n - nth value in sequence
- a - initial value of sequence
- d - difference in each value
- l - last value in sequence

Look at the below example and get a clear idea on how to solve the sum of linear number sequences with detailed solutions. Learn the concept thoroughly and verify your answers using our** free online Sum of Linear Number Sequence Calculator - Handy & Free Online Tool . **

For quick calculations of any specific number in a linear number sequence refer to our **sequence calculators'** offered free online arithmetic sequence calculator.

**Example:**

Let's consider the following input values and find the difference and sum of the linear number sequence.

Initial Value = 2

Periods = 5

Final Value = 10

**Solution:**

Given inputs are Initial Value = 2, Periods = 5, Final Value = 10, Difference=?

To find the difference, apply the formula ie.,

Difference = (Final Value - Initial Value)/ (Periods-1))

By substituting the input values in the above formula, we get

Difference = 10-2/(5-1)

Difference = 8/4

Difference = 2

Now, calculate the sum of the linear number sequence by using the formula ie.,

S_{n} = n/2(a+l)

= 5/2(2+10)

= 5/2(12)

= 30.

Hence, the sum of linear number sequence 2, 4, 6, 8, 10 is **30**

### FAQs on Addition of Linear Number Sequence Calculator

**1. What is the formula to find the sum of linear number sequences? **

The formula to calculate the sum of the linear number sequence is S_{n} = n/2(a+l)

**2. How to find the summation of linear number sequences? **

The steps to find the summation of linear number sequences is explained efficiently on our page with examples.

**3. What is the Sum of Linear Number Sequence Calculator - Handy & Free Online Tool ? **

Sum of Linear Number Sequence Calculator - Handy & Free Online Tool is a free online tool that helps students to solve complex linear number sequences in just microseconds and display the output with steps.

**4. Where can I get a free online linear number sequence calculator? **

SequenceCalculators.com is a reliable and trusted calculator website that provides all sequences calculator like Arithmetic Sequence, Geometric Sequence, etc. So, you will find the free online Sum of Linear Number Sequence Calculator - Handy & Free Online Tool s from the portal.