# Sum of Integers Formula

Before learning the sum of integers formula, let us recall what are integers. Numbers without fractional or decimal components are integers. The sum of integers can be calculated by doing simple mathematics when the numbers to be added are less. But if it is required to add many consecutive integers at a time, we use the sum of integers formula. It simplifies our calculations involved and minimizes our time of addition.

## What Is the Sum of Integers Formula?

The sum of integers formula is nothing but the sum of n terms of an arithmetic sequence. The sum of integers formula is:

### Sum of Integers Formula:

S = n(a + l)/2

where,

- S = sum of the consecutive integers
- n = number of integers
- a = first term
- l = last term

Also, the sum of first 'n' positive integers can be calculated as,

Sum of first n positive integers = n(n + 1)/2, where n is the total number of integers.

Let us see the applications of the sum of integers formula along with a few solved examples.

## Examples Using Sum of Integers Formula

**Example 1:** Find the sum of integers from 1 to 1000.

**Solution:**

To find: To find: Sum of integers from 1 to 1000.

Given,

n = 1000

a = 1

l = 1000

Using sum of integers Formula,

S = n(a + l)/2

S = 1000(1+1000)/2

S = 1000(1001)/2

S = (1001000)/2

S = 500500

**Answer:** Sum of integers from 1 to 1000 is 500500.

**Example 2:** Find the sum of integers -3, -2, -1, 0, 1, 2, 3, 4.

**Solution: **

To find: Sum of integers from -3 to 4.

Given:

n = 8

a = -3

l = 4

Using sum of integers formula,

S = n(a + l)/2

S = 8(-3 + 4)/2

S = 8(1)/2

S = 4

**Answer:** Sum of integers from -3 to 4 is 4.

## FAQs on Sum of Integers Formula

### What Is the Formula to Calculate the Sum of Integers Formula?

The formula to calculate the sum of integers is given as, S = n(a + l)/2, where, S is sum of the consecutive integers n is number of integers, a is first term and l is last term.

### How do you Find the Sum of all Integers From 1 to 500 Using Sum of Integers Formula?

The sum of integers from 1 to 500 can be calculated using formula, S = n(a + l)/2. Here, n = 500, a = 1, l = 500. ⇒ S = 500(1 + 500)/2 = 125250.