Before discovering the amount of integers formula, let united state recall what are integers. Numbers without fractional or decimal componentsare integers. The sum of integers can be calculated by doing straightforward mathematics as soon as the numbers to be added are less. However if it is forced to include many continually integers in ~ a time, we use the amount of integers formula. The simplifies our calculations involved and also minimizes ours time of addition.

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What Is the sum of Integers Formula?

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

Sum of Integers Formula:

S = n(a + l)/2


S = sum of the continually integersn = variety of integersa = very first terml = last term


Also, the sum of first 'n' hopeful integers have the right to be calculation as,

Sum of an initial n confident integers = n(n + 1)/2, where n is the total variety of integers.

Let united state see the applications that the amount of integers formula together with a couple of solved examples.

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Examples Using amount of Integers Formula

Example 1:Find the sum of integers native 1 to 1000.


To find: to find: amount of integers native 1 to 1000.Given,n = 1000a = 1l = 1000

Using sum of integers Formula,

S = n(a + l)/2

S = 1000(1+1000)/2S = 1000(1001)/2S = (1001000)/2S = 500500

Answer:Sum that integers indigenous 1 to 1000 is 500500.

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


To find: amount of integers indigenous -3to 4.Given:n = 8a = -3l = 4

Using sum of integers formula,

S = n(a + l)/2

S = 8(-3 + 4)/2S = 8(1)/2S = 4

Answer:Sum the integers indigenous -3 to 4 is 4.

FAQs on sum of Integers Formula

What Is the Formula to calculation the sum of Integers Formula?

The formula to calculation the sum of integers is provided as,S = n(a + l)/2, where, S issum the the consecutive integers n isnumber the integers,a isfirst term and l islast term.

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How carry out you discover the amount of all Integers native 1 to 500 Using amount of Integers Formula?

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

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