Before learning the amount of integers formula, let united state recall what space integers. Numbers without fractional or decimal componentsare integers. The amount of integers can be calculate by doing basic mathematics once the numbers to be included are less. Yet if it is compelled to add many consecutive integers at a time, we usage the sum of integers formula. It simplifies ours calculations involved and also minimizes our time the addition.

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What Is the amount of Integers Formula?

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

Sum the Integers Formula:

S = n(a + l)/2

where,

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

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Also, the amount of very first 'n' positive integers can be calculate as,

Sum of very first n hopeful integers = n(n + 1)/2, whereby n is the total variety of integers.

Let united state see the applications of the sum of integers formula in addition to a couple of solved examples.



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Examples Using sum of Integers Formula

Example 1:Find the sum of integers from 1 come 1000.

Solution:

To find: come find: sum of integers from 1 come 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 from 1 come 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 -3to 4.Given:n = 8a = -3l = 4

Using amount of integers formula,

S = n(a + l)/2

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

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


FAQs on amount of Integers Formula

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

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

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How carry out you discover the amount of every Integers from 1 come 500 Using amount of Integers Formula?

The sum of integers indigenous 1 come 500 have the right to be calculated utilizing formula, S =n(a + l)/2. Here, n = 500, a = 1, together = 500.⇒ S = 500(1 + 500)/2 = 125250.


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